Well we stay right on the beachfront at the Marinaki. They have everything you could need for self-catering (not that we have ever used these, due to the fabulous eateries in Arillas!). We also have 3 boys (8, 8 and 12) and find these more than adequate. The Kaloudis, Rainbow, Horizon, Irene Villas or Mirage would also probably be ideal. I'm sure if you check the accommodation pages out you will find the perfect place.
Good luck!! One question, how on earth have you managed 4 years without the kids?!