I don’t think it is rebellion, I think it is confusion, which in teenage years of course there is usually some friction with family, but I would not call it rebellion, he is not sure himself of what he wants to do. He rejects your lifestyle (but it seems to me he is committed to judaism, which is a huge blessing) but he has no alternative! Listening to that music is not a lifestyle, it may be something we do on the subway (or we may prefer reading, or whatever) but can not define an identity, no matter how many hours a day is done.
He does not want to daven? Tell him “there is no jew who does every mitzva, there is no jew who does none, so, we are all in the same middle ground”. What you should do, is to enable him to daven and do mitzvot without feeling embarrassed, whenever he wants to (I suspect it accounts for most situations, and possibly to all) so that he can be observant (at least, as much as he wants to) and all that while retaining his self-image that he is independent, adult (he actually is), and different from a surrounding which, for some reasons that so far you don’t know, he feels as oppressive. If it is necessary, let him call himself non-haredi…. no big deal. Yes some fools may say a word or two, if so, proudly introduce to someone else in front of them your non-haredi boy, and they will shut up once for all.
You’re lucky w.o.w. that you did not go through these difficult “growth pains” when you were his age 🙂 most people do, and sure I did. I suspect most rabbis too, would relate, but what do I know, I am no rabbi 🙂 yet, don’t dismiss that a rabbi may have been through the very same experience, possibly his own rabbis and teachers.
Not sure if I can check again before shabbat, either way, shabbat shalom to you and all your family. And to your son’s friends too.