How about going to France with Europcamp, this is a genuine self-catering holiday, as opposed to others where basically people hire an apartment and eat out all the time, as opposed to going in a hotel. A family of 5 eating our every night even in a cheapish place like Turkey will cost you quite a bit of money. You would probably need to allow 100 pounds a day for the five of you on top of your accommodation.
You can either go by ferry or euro tunnel to France and stay in a mobile home. All three of your children will be free, as you only pay for the hire of the mobile, you can get different types of mobiles some more upmarket than others, depending on your budget. You may also be able to go by coach as you did with your holiday to Spain.
Most sites have lovely swimming pools and laid on activities for children the ages of yours. It's all very laid back with people shopping in local supermarkets, buying local produce and tending to have lots of picnics and BBQ's (you need to check site details to see if they allow BBQ's). You can pick either beachsite sites or countryside sites.
There is no need just to stick to Eurocamp, there are many other companys that offer these kids of holidays like Frech Life. You will need to go towards the south to pick up good weather though.