Have you got Alastair Aird's The Good Britain Guide (link to Amazon )?
It covers the whole of Britain, it lives in our car and it's given us dozens and dozens of fabulous ideas. You can get bits from it on the website - goodguides.co.uk or something like that - but not everything, I expect.
Sorry, may be too late now but there is a swanery at Abbotsbury which is good for children. They normally have some cygnets there though it may be too late in the year for them to be in the cute stage now.
Also Lyme Regis has a dinosaur museum (was a bit tacky when I lived there 10 years ago but may be OK now), also lots of rock pools and fun to be had looking for fossils.
If you are prepared to drive a bit further into Devon, Beer is a lovely village, with a model railway place called Pecorama and some old quarry caves which have guided tours, real fishermen on the beach and some good pubs. Also the Hook and Parrot on Seaton seafront used to be very good.
Just a bit further along is Sidmouth which has a big donkey sanctuary on its outskirts.
Finally Bridport used to have a very good farmer's market on a Saturday - Hugh Fearnley-Whittingstall from River Cottage sometimes has a stall.
Kingston Maurward Animal Park is nice (near Dorchester). Also has stately home and big lake. Highly recommend Pecorama near Beer (as in previous post). Beaches like Burton Bradstock, Seatown. Dorset (not Seaton, Devon), Eype, are all unspoilt and beautiful, but shingly. Weymouth is a much larger resort (and sandy) but great for the kids with a land train that goes along the sea front to an aquarium, and lots of fairground ride (small scale and old fashioned) on the beach.
Highly recommend the Riverside Restaurant in West Bay. It specialises in fish, they have lovely food for children, and are family friendly. I found it because I was reading Notes from a Small island by Bill Bryson and he went there in the book and raved about it. It is set back from the seafront, and although might look fairly ordinary from the outside, the atmosphere is great inside. It is a special treat though as it is quite expensive (2 adults and 1 kid 3 courses + bottle of wine about £75 I seem to remember in 2003). This might blow your budget? West Bay is just along from Eype, and not far from Lyme etc.