My suggestion would be to go self-catering inthe Marmaris/Icmeler area, which would probably suit your restless teenagers no end, and your budget is okay, for we have done 2 weeks peak season for less.
Would recommend Marmaris for the teens, as it is all geared up to the younger age groups, but depends how much you like a brash 'in your face' bustling resort, fact is we hated it, but can see how much it must appeal to the teens.
However, if you don't like the sound of Marmaris, stay in nearby Icmeler, a different kind of animal altogether, with a far more laid back vibe, better beaches, and in my opinion a much prettier location, surrounded by the pine forests of the National Park. The good thing about staying there would be that you can all just hop on a dolmus (bus) and visit Marmaris, which is a short ride away and cheap enough too, so that you keep the kids happy, as well as being able to spend time chilling out on the lovely beaches in Icmeler.