I'm also an apartment-lover. Last year we stayed at an apartment at Odyssey Residence - lovely, spacious and modern apartments, but appalling hotel management (multiple instances of overbooking/random or non-existent room cleaning and changes of towels), so that's out.
We had a look at Diana Residence whilst we in Calis last year and I think it ticks all the boxes. Lovely, HUGE modern apartments, plenty of AC units, washing machine in the apartments, kid's pool. The staff seemed very friendly too. We had a chance to speak to some of the residents and many were on their second/third visit. All gave the thumbs up. Crucially, the hotel is of a size where there will be other kids for our kids to play with (and so give us a bit of relative peace and quiet). It's about a 5 minute walk to the Dolmus station/Guven's restaurant, but dolmuses pass by outside the next-door-but-one Odyssey Residence every few minutes or so in any case. The upside of the relative remoteness is peace and quiet. If you can get my 11-year old daughter to walk the distance to Guven's, you really could get anyone to do it.
We've gone for a humungous 3-bedroom place (ooh look at me! - very reasonable price, given the standard, though) and are really looking forward to it. I believe that the 2-bed apartments are situated on the ground floor but you might want to check that first.