We went a few years ago and stayed at the White Horse campsite - right next to the huge carved white horse in the slope. Lovely campsite, pretty basic as that’s what we like, eweleaze looked great fun but much busier. Might be handier with a shop and food options for you with little ones though - but white horse was brilliant for acres of space.
Great day trips -
Loved the Abbotsbury subtropical gardens. There were Alice in wonderland sculptures all over the place when we visited, and even if that’s changed, it’s a really nice place to wander around with kids. Great on a windy cool day too as it’s genuinely warmer and more sheltered than elsewhere!
Lyme Regis - lovely but massive honeypot busy town. Arrive EARLY. Can be a nightmare with traffic. But gorgeous. If they like fossils, there’s a spectacular ammonite pavement along the beach - park at Monmouth beach car park and walk along the beach towards “Lyme Regis fossil beach” but you have to go at low tide or it will be all covered. See pic attached.
Chesil beach and Portland are worth a trip -‘don’t try to walk along chesil beach but you can park next to it and walk up to the top to admire the massive bank of stones! There’s a sculpture place at the quarry on Portland as well which could be fun for kids to scamper around.
We had a few rainy days, so were grateful for the basic quick fun of the pirate adventure golf and the sand sculpture place next to the aquarium. There’s kids go karting as well. Sand sculpture place is really good!
Weymouth beach is great - large, lots of stuff for kids to do but just a good beach anyway. Lovely sand. I probably wouldn’t bother going over to swanage as well if you’re at Weymouth - both are great but might as well stay local.
Good local coast walks around Osmington, start and / or finish at the Smugglers Inn (book a table perhaps as it gets busy).