Well, yes I've lived on Ibiza for 40yrs so know most of it. btw stay out of Cala San Vicente, it's a lovely place, beautiful beach but all German, not that I have any problems with that, but you don't want to stay in a German only speaking hotel - I think tui (Thompsons) use them. Nice for a day trip and lunch though.
There is the Hotel Orquidea in Sta Eulalia which does cater for kids, is rather big, and has fun nights, but tends to be a bit rowdy. They are small apartments, that should be OK, it right on the beach of Sta Eulalia. There is an all-inclusive hotel in Cala llonga called Sirenis Playa (something can't remember) but that can get a bit rough , hamburgers, chips ice-creams and drinks free most of the day, with entertainment , hence lots of drunken Brits. Not far from S:E; and a good bus service and also boats. you do don't go to the Hotel Riomar in S. E: I know that they use up old out of date food (cos my daughter worked there and it was disgusting) Good luck.