We actually had really good weather and I've just checked metcheck for next week's weather and it looks fine for you. You may get wet putting the tent up but after that it seems ok.
The steam train to Swanage past Corfe Castle should be ok in the rain and the station is right in the middle of Swanage so you can get to the sandy beach if it's ok.
We also went to Brownsea Island (NT to get onto the island but you have to pay for the ferry)which would be ok on a showery day as the walks are mostly through the trees, watch out for the peacocks, they were determined to get our picnic!
Not sure about Monkey World as we didn't go there. Our two liked Kimmeridge Bay, you can go crabbing there and look for fossils on the flat rocks, that would be ok on a showery day too as it's not a 'typical beach'
As you can tell we liked to do the outside stuff, Studland Beach was lovely, thanks for that recommendation and we walked along the cliffs to old Harry Rocks, dd2 needed a piggy back on the way back!
We also went to Lulworth Cove and Durdle Door, fabulous, but what a hike, I wouldn't do that with little ones.
Tyneham village is really interesting, dd1 (age6) liked the stories of the village on the boards in the deserted houses.
I hope you enjoy the site as much, we found the owner rather grumpy and some of the 'regular' caravanner's children ran amok on the playground and broke the big trampoline!!
Our pitch was lovely though, down amongst the oak trees. I'll try and find a picture of our tent to post later!