We stayed in Kaya every year for about 10 years, twice a year if we could afford it.
We used to stay at Muzzys place, so had their pool and the kids used to love the waiters and having other guests around.
To be honest I think they would have got bored in a villa. It's nice to have company, other people to chat to, other families visiting the pool etc.
We never found getting out and about a problem, dolmus every half hour and we used to go out alternate days, either to Olu, into Fethiye, to Gemiler beach etc
You need to get a dolmus to the beach. For Olu you go up to Hisaronu, then change to go to Olu Deniz, it's pretty straightforward.
The Gemiler dolmus is very infrequent, I think only 11am and 3 pm, although that may have changed.
On the Kaya days we often would go out for a walk, go for pancakes in the village, and got to know a Turkish couple, and crazy as it sounds we used to love going up the mountain with him at the end of each day and give the goats water etc.
Evenings in the village were quite low key, either staying chatting with new friends, trying different restaurants for dinner, or going up to Hisaronu.
If we missed the last dolmus Muzzy used to send someone to come and get us, sometimes we used to go out with him and the staff after hours up to Hisaronu to the bars and go dancing.
Once they got quite a bit older we started to stay in Calis, so then they could go out in the evenings and come home together, or with friends they brought over on holiday with them.
We never had any problem with any tour companies picking us up, apart from one morning at 6 am waiting to go to Pammukale, when they forgot to come and get us, but that could have happened anywhere, I'm not sure about boat trips as we used to get the bus down to Fethiye or Olu for boat trips.
Hope this helps.