With three young DC I would recommend.....
Going to amble paddling pools. It's a small beach in amble enclosed by a pier so not got crashing waves and it's very shallow.
On the other side of the pier is a great spot for rockpooling at low tide. You can get buckets and nets from amble.
Warkworth castle is nice and they usually have things going on over the school holidays-falconry, fighting knights etc
A walk down the river at Warkworth in the evening is lovely. Feed the ducks and have a relaxed walk-you can walk around the castle in the evening too (outside the grounds) and it's lovely and peaceful in the evening.
There's a coastal path that's good for riding a bike on if you fancy that? You can get on at Warkworth and go along up to alnmouth to spend a day there. The village is nice as is the beach.
I would definitely recommend getting a national trust and English heritage membership for up here. Family passes are less than £10 a month.
Cragside is also lovely. Great walks. It's huge too so even when it's busy you can do a walk there and see very few people. The labyrinth and the play area are good there-den building too. Take a picnic and you're set for the day.
The puffin cruises are in late June/July. Take hats though as there's lots of flying birds = bird poo 
Kielder national park is also gorgeous.
A lot of the towns/villages have local shows/raft races/markets so look them up too. Warkworth have just had a Warkworth show, alnmouth raft race etc
Imo evenings are the best on the beach. A little bbq. Maybe a walk down the coast a little.
I'm a new local and love it up here.