You want a Hyatt with a nice pool and a park nearby, and no shenanigans needed to book 3 to a room. The best one I've been to is the Grand Hyatt Istanbul.

It's cheap on points, the SUA gets you a big Grand Suite, the pool is really nice, food is easy in the Grand Club, there are two parks with playgrounds (and friendly feral cats if you're comfortable with that) right behind the hotel, Turks love kids, and you can fly directly to Istanbul from any major US airport. My wife swears by flying Turkish with young kids, for what it's worth.