I don't know a great deal about Dartmouth, but I can give you a lot of information on North Cornwall - where I live.
The Minack theatre is a great day out, however it is a very long trip from Bodmin especially with children who may get restless. The Eden project is a great idea & it's not too far from Bodmin. Bodmin town hasn't got a great deal on offer. No beaches, theme parks, land marks or anything. The only decent thing about Bodmin is Asda & Morrisons which we don't have in Wadebridge where I live.
Suggestions:
-Between Bodmin & Padstow and wadebridge in between you have the Camel Trail. Where you can walk or take bikes and cycle from each town. You can hire bikes so you don't have to take your own. It is a lovely scenic walk or cycle & both trails are nice but the wadebridge-bodmin one is more sheltered, quieter & more historic scenerys such as old train platforms. The trail also leads to other destinations. The Padstow one has a lovely view of the river camel, but it is a lot busier & doesn't have any turn offs to other places.
-Bodmin moor is a huge area of countryside in the villages surrounding Bodmin (Blisland & St Breward). There are several places where you can stop and children can play in the stream, where it is quiet and much safer than the beach.
-Near Wadebridge there is Crealy Adventure park, a large theme park with indoor play areas, slides, a log fume, water slides, walks & rides etc, a great day out for kids. From Bodmin this will take roughly 25 minutes.
-Ferry from Rock to Padstow or vice versa. There is a small passenger ferry between Rock & Padstow. Both areas are lovely with great beaches & shops so you can park at one place & catch the ferry to the other and back again. It is a lovely little day out. You also get a lot of famous people around the Rock area so look out for them!
-There is a castle at Lostwithiel which is only about a 5/10 minute drive from Bodmin. I think it is called Restormal castle.
-There are no outdoor water parks in the area. However there is a large swimming people with some slides at Hendra Oasis near Newquay.
-World in minature near St Agnes. It displays minature landmarks from around the world, which is very interesting. It also has a few play areas & rides.
-Springfields pony & fun park near Bodmin is a small, friendly & relaxed theme park. It has pony rides, trampolines, go karts, rowing boats, animals, a play area, parks, walks & lots more.
There is lots more in the area! Just pick up some leaflets from a tourise information centre or from a supermarket.
Have fun on holiday :)