I'm sure they're fine, but the name Brilliant Apartments tickles me... hope they live up to their tag...
15 and 17 year old will probably love it, lots of things to do in the Protoras/Agia Napa area - waterparks etc. Good beaches around there too.
From Protoras I would guess that you could drive to Paphos in about 2.5 hours, so if you don't mind 5 hours spent in the car it's within a day's reach. If you want to explore the Paphos area more, I'd probably find somewhere that you could stay overnight to get two days around there.
Wouldn't bother with Limassol, there isn't much there that you can't already get in Protoras/Agia Napa... really more of a commercial city than touristy per se.