If you're visiting Disney parks then, hands down, I'd stay at either the Swan or Dolphin. The pool is really among the best "on" Disney property (I realize they aren't owned by Disney). You can't beat the boat to Epcot and Disney Studios or the close proximity to Boardway (night-time entertainment?). There are several restaurant choices as well. Our room at the Swan was large (bigger than Disney resort size). It did have a stocked mini bar though so I would request alcohol removed if you have concerns with teens. I'm not there yet as my kids are still young--lol. I think Gaylord, while beautiful, is kind of isolated from everything. I mean, there is really not much near it at all. It's bit tricky to get to too, IMHO. When coming from Disney we got turned around a few times. Now, I have to stress we didn't sleep there, just went for the ICE! show in November, toured a bit of the hotel. It's beautiful but I'd rather stay on Disney property if Disney were my focus.
HTH!