First of all, my heart goes out to any mom (or Dad) in this situation.  It is nothing less than heart-breaking, not to mention frustrating when you don't have a clue as to what to do to turn things around!  I pray this will be a time during which you'll draw close to the Lord like never before. Not that you haven't!  It's just that I think this is what "going from glory to glory" is about;  it only gets better and better! ... And I pray, too, that you'll receive from the Lord comfort, direction and practical steps to take.  If you recognize your neediness, then you are in a very good place already!  God is not free (or asked) to intervene until and unless we recognize our inability to fix it ourselves.

You asked:  "Is it possible to get a burned out teenager with a bad attitude about homeschooling on fire for learning (at home)?" ...  Let me first say that if there is any hope for this to happen, it will not be in finding the right curriculum or resources!  You will need to start with his heart. You know this already, but it's so important that it bears repeating. This will involve a lot of heart-to-heart talking, prayer, searching your heart and his, prayer, waiting on God.
   
You also said:  "My teenager enjoys school at the public school."  This should not come as a surprise.  Very few, even spiritual-minded kids, don't enjoy the public school scene.  It is a setting that any "normal" kid is going to love, unless they are either socially or academically ill-equipped for it.  (Which explains why I didn't like it!)  So don't wait around for your child to get excited about homeschooling.  Kids do not typically choose wisdom.  (Just take one down the cereal aisle and ask what they want!)  It's only after our "faculties are trained" that wisdom emerges; until then they will "walk by the flesh." This is actually true of all parents as well! 
     
I suggest that you begin by listening to the Effective Parenting of Teens seminar by Pastor Reb Bradley of Family Ministries which will help you get to the very heart of some important things, both in you and in your son.  You do realize, don't you, that home education is more about the parent than it is the child?!?  Yes, we want to educate our children, but what's in the mind of one bus driver is going to impact the entire busload of people. 

Intersperse your own reading with talking with him, using his walk with the Lord as the focal and motivating point.  Does he love the Lord?  If not, that's where you need to start; if so, then he's going to want to follow Him and His way.  You, as the parent, have been placed over him for this season of his life for a reason ~ a good reason.  The anguish you are feeling in your heart did not come from the world, but from God.

Talk about what he wants in life and how he thinks he's going to get there.  And please do not revert to "submission to parental authority" here to make your points.  Yes, this is important, but if you want to engage a child's heart and mind, you need to appeal to his walk with God, not just the "rightness" of obeying you.  God honors that, of course, but to grow into maturity, your child, more than anything, needs to be discipled and gain understanding, not just walk in what is right or what he feels he wants. 

Marilyn Howshall's book Wisdom's Way of Learning along with just about all of her new books may help even more than Parenting Adolescents at this point.  (It depends on your particular need.)  They will all eventually come into the picture, I believe, but let God show you how to proceed. More on this in a moment...

   
You might also read our daughter's letter here at my website. She wrote an encouraging letter to a reluctant homeschooled boy  on homeschooling through High School ~ a boy who did not want to homeschool anymore.  There may be some helpful ideas there, especially for your teen.  But it's going to take more than "inspiration and good ideas" for Mom!

   
Going on with your questions:  "Am I supposed to give up my ideals for his education and concentrate on my other children now?"  I doubt it.  You will just need to proceed differently than if he were younger.  Read, pray, talk, pray, read, talk, pray... get into his mind and heart. You can't just tell an older child that "this is the law, just DO it!"  It might be the best thing for him, but it won't work. They need to be "brought along," not "bullied."  

You may need to change how you speak to and with your child(ren), perhaps even your younger ones.  (That may be where some of the trouble started.)  When I hear basic conversations between parents and their children, I think "No wonder!" that the children now have bad attitudes!  Disrespect  is so common!  I trust that the Lord will start speaking to your heart about this.

Another thing commonly lacking is physical affection.  This can do wonders for a relationship and can heal and bond.  A child never outgrows his need for this, but sadly too many become "too cool" for it.  Thus a huge vacuum is created that most kids seek to fill with premature (literally) relationships with the opposite s_x.*  And by "premature," I mean "before maturity."  I personally believe that the only kind of relationship kids should have with the opposite s_x before they are mature enough to be getting married is of a "brother-sister" nature.   (More on that in the "Romance & Relationships God's Way" section of the Article Chart.)  I have been so delighted to see our older two children remain just as affectionate with both Dave and me.  Tory (our 20-year-old son) still lays on his dad and even sits in his lap (mostly for fun) sometimes!  Sharnessa sits in his laps with total seriousness!  And both love backrubs from me, and I love getting them from them to!  None of this is forced, but feels very natural and sweet.

If your student is burned out on too much "school at home," I suggest that you allow him or her a time of "debriefing."  Janie Levine Hellyer has written an excellent article on "Bringing Them Home" that you will gain much from.  And Marilyn Howshall talks about this in various places in her writing. There's not just one single, best book on it; but you need to hear everything she says anyway, not just her thoughts on "this thing or that."  Part of the cause of the burn-out and rebellion is due to wrong attitudes about education.  If this is not fixed, nothing else will do much good because you'll still be caught in the same maze that is causing the problems in the first place! 

   
I can't stress that enough that some sort of "Season of Re-education and Renewing of the Mind" would make all the difference in the world for you.  In fact, if all parents would begin their homeschooling experience with such a season (or any rendition of it that God may lead them to), there would be little if any teenage rebellion and burn-out in later years.  

Have you noticed that rebellion in the teen years is actually expected!?!  What a shame this is, reflecting a gross lack of understanding of the heart of child raising and training!  It is widely accepted that rebellion is as natural and expected as puberty, and is a "healthy" part of growing up!  Nonsense!!!  It is natural and "to be expected" only if foolish parents expect it and do not take the time to seek God, yield their own hearts to God, and "study to show themselves approved" in this area. 

And I don't mean just one "psycho-babbly" book brimming with today's short-sighted, supposedly "modern" ideas.  There is some truth in today's psychological counsel, and I realize that much of it came out of a repulsion for too-strict and legalistic approaches to child raising that were touted as "biblical" and "godly."  The only way for anything to be truly biblical and godly is for it to be founded on love, grace, and wisdom.  Aside falling short of that automatically loses that title.  

But unfortunately too many kids were raised by "pseudo-godly" parents, who were "holding on to a form of godliness, but denying the power thereof" ~ namely the power of love.  And so these embittered and disillusioned children, instead of seeking the truth of God, sought the world for its solution.  Unfortunately, it just doesn't work either.  Only a return to a complete surrender to God and to seeking His ways and His heart can produce good fruit.  

And as I mentioned, it's going to take more than reading one good book on the subject.  It's going to take a focused season.  There are many aspects of this season, many areas that will need to be covered and recovered, and often much ground that needs to be recovered as well.  The "obvious" need is to focus on child training books, and they will surely be part of it.  But be open to God leading you to ones that are more "spiritual" in nature, because that is commonly the root cause of the problems between parents and their children, not so much the external expressions, which we tend to focus on.

So start with prayer, and then proceed to some resources that you sense God leading you to.  Changing the Heart of a Rebel is good, and so are Shepherding a Child's Heart and The Key to Your Child's Heart.  

If finances are tight, pray for God to bring about people who have the books that you could borrow. (Just to warn you, very few of them are going to be found in a public library; they are "off the beaten course," which explains why "the beaten course" is so well-trodden with rebellious feet!)  Or you might pray for God to lead you to someone who'd want to go in with you and purchase materials together so that you can share ~ and split the cost of ~ the resources.

(By the way, I did not start out thinking "Hmmm, how can I sell something to homeschoolers?"  I have been counseling people ~ one-by-one on the phone, and at my seminars ~ in the direction of these resources and such a season for many years now, and have only recently finally come up with a basic (generic) outline for it, and a syllabus to use as an "alongside guide" and journal. We decided to start selling the books for this season ~ which include several of mine and several by other authors I admire ~ when I realized how many people were having a hard time locating them, or were overwhelmed at having to hunt them down from so many different sources.)

   
Let me add that if you want it to actually make an impact on your life, you will need to enter your "season" with a sense of going through it with God, not ahead of Him, seeking Him for direction and the order to do it in.  If you enter it with a heart to "just get it over with" or to merely "find out how to whip your straying, rebellious child into shape," I assure you that you'll get nothing out of it, so don't even bother starting. 

God is very personal and specific, so the more you hear His voice, the more tailor-made this season of coming out of the "hard place you're currently at with your teen" will be for you.  God is considering your needs and the place your child is at, in relationship to God and to you.