Some great suggestions here OP
My own suggestions would be to definitely not bother with AI- I'm not that pro them anyway as I think it gets boring eating and drinking at the same place and is shit for the local economies , but it works much better if you have older children- otherwise you end up paying through the nose.
Cruises can be good value and the right ones have lots for little ones
Eurocamp is brilliant and good value if you are ok with upscale camping or lodges and can drive- as someone else said either drive to it with your car or fly in and hire. These have been some of my favourite holidays
EasyJet holidays have some good packaged up options and use some good hotels too at a good price
Booking.com is brilliant for just nosying around and reserving without paying- whilst then seeing if you can get suitable flights. Very often you don't pay till a few days before too, so good if you are saving up rather than fully having the money 'right now' and is good as well if you change your mind as you haven't paid!!
My favourite places with young ones would be
Puerto pollensa , camp de Mar and Cala d'or in Majorca
Can Bosch and Cala n forcat - menorca
Santa Eulalia or Es Cana- Ibiza
Corfu- kassiopi or Paleokastritsa
South of France- Eurocamp has loads
Brittany - Eurocamp or lots of gites
Algarve- carvoeiro