I have been looking at holiday rentals in Turkey and there are two types of self-catering accommodation - villas and apartments. There are some places which would be large enough for you all - some of them consisting of a pair of adjoining self- contained dwellings with a shared swimming pool.
The best place to start looking is on Trip Advisor - for descriptions and reviews of properties plus things to do, etc. If you go to the forums, you can get advice from people who know the area well. Once you have selected your destination, just click on the " More " button.
Does it have to be Istanbul ? We will be flying to Antalya and staying in Kas and Cirali/Olympos which are both still unspoilt, embraced by green mountains and blue ocean. The word " turquoise " to describe a certain shade of blue actually comes from this Turquoise ( Turkish ) Coast ! *
Because Kas is three hours from the airport it isn't overrun by tourists. The visitors who do go there are from many different countries ( and from Turkey ! ) Kas is a lovely town with cobbled streets and Ottoman houses: it's the site of Antiphellos and is on the Lycian way with wonderful walks. There are restaurants, etc to suit all budgets and tastes. It is one of the best diving locations in the world and there are many other activities available such as kayaking, boat trips and even paragliding ...
And of course, you are surrounded by the remains of many ancient civilisations :)
If I was going with a large group I would want to stay at " Villa Be Happy " which looks amazing: a renovated village house with a hammam and an infinity pool in a beautiful natural setting. It is the biggest villa I have found but the rates are half that of places on the peninsula. It is listed on TA and on Owners Direct.
I also recommend looking at Patara ( Gelemis village. ) The beach is incredible and is a protected area - for the turtles, and because of the ruins of the Lycian city. You can canoe down the river to the beach, or ride there on horseback over the dunes : ) Or get a lift from a tractor with a trailer !
Patara is friendly, peaceful and inexpensive: there are several family-run pensions where you can get a double room with breakfast for under thirty euros a night.
It is near Kalkan, ( where you can go on a boat trip for the day for twelve or fifteen euros; go diving, etc ) and a bit closer to Dalaman airport than it is to Antalya.
If you prefer to stay somewhere more touristy and closer to an airport, Dalyan and Olu Deniz are close to Dalaman, while Lara Beach, Side, Konyaalti Beach and Kemer are all close to Antalya.
Antalya is not as big as Istanbul, but the Ottoman old town ( Kaleici ) has a beautiful harbour, mosques, hammams, bazaar, museums, restaurants, etc.