Hello
Very difficult isn't it...........but it can be done. I can only suggest AI hotels, (sorry) that's all we have ever done in Turkey, and we took our "Little Uns" with us, up until 6 years ago, so I can suggest a few that may be of interest.All have family rooms or suites, a couple have villas, I know cost is something we have to keep down with a young family, but, some Travel Agents will price match, and some Tour Companies do have some deals on at the minute, so worth checking all the sites for deals.
Flying into Antalya.
Lara Beach Region.
Concorde DeLuxe
Limak Lara
Kervansaray Lara Resort.
Belek Region.
Papillon Zeugma
Papillon Ayscha...........Both these hotels have family villas, they are superb, and the facilities here for children are second to none.
Club Asteria.
Flying into Bodrum
Turgutreis Region
La Blanche Hotel. (again, superb rooms and facilities for children)
Kadikale Resort.
Voyage Torba. (Wonderful)
Kefaluka Resort and Spa. (newly opened in 2009, so may be some good offers?)
I have suggested the above hotels mainly because of the ages of your children, and the fact that there isn't a great deal of travelling time once you have collected your luggage. Longest distance is thru to Turgutreis (about an hour) the others between 20 and 40 minutes, Lara Beach being the nearest to the Airport in Antalya, have to consider everything when you have little ones. (ain't that the truth?)
All the hotels have good facilities, little clubs, playgrounds, excellent staff, kiddies pools and most offer a baby sitting service (small surcharge).... if you do require other board options, then I know others will be able to help.
Hope you get what you want, and if you need any more advice then please, shout up.
p.s. Ask when booking that you are getting a family room, not a room that sleeps 4. These can be cramped unless specified.