unless i missed it you dont mention what airline you are flying. I believe you would have to be flying a star alliance airline or of course Turkish airlines. You would need be *gold or travelling on a business class or first class ticket. There is an up escalator when you arrive past immigration that leads to the airside international departure gates but I had to show an intransit ticket to an agent before i could go up the escalator. It is worth a try.

On arrival if you just clear immigration, you have to walk to the next terminal( 5 minutes) that handles domestic flites. there is a Turkish Airline club in that terminal. No where as nice as the Intl one. It does have a nice spread for breakfast food and a private shulttle bus from the club right to the plane! kind of nice