There are plenty of sites on Angelsey with play areas for kids. We have narrowed it down to two - one for the end of May, and the other for the end of August. Both family run parks, with children's play area. Both with good reviews. So we are off to try them. We've gone for Ty Hen in May and Kingsbridge in August.
I decided that I wanted to go to Angelsey this year, so looked on Campsite Search - narrowed it down to about 7, then went for a list in order.
You could try Bodfan farm at Rhosneigr, thats a great site for kids your age, tons of room, Shoreline camp site, also in Rhosneigr is ok, but you need to get on the tent only field as the rest of the site is hemmed in with statics.......
Home Farm is nice for caravans lovely clean campsite with small shop & excellent facilities. Your children may find the outside play area a bit limited but it has a big field & football pitch