Tricia, I moved here a month a go and have an 18 month old! I have been looking for things for us to do too!
Warrington council website has details of the pools. They seem to have parent & baby sessions on different days (Fordton today for example so I may take DD).
Where abouts are you? My searches have all been around WA4 but I've found softplay (Latchford), Cafes where children can paint on ceramics (Stockton Heath & Latchford), Walton Hall Childrens Zoo, lots of mums & tots groups, Stockley Farm, Applejacks farm/adventure type place.
Sorry for the lack of links. DD is emptying the kitchen drawers as I type!
I don't know either of those parks, are they near Stockton Heath?
I'm taking my 18 month old to the ceramic cafe this week - I have a feeling I'll regret it but I'm meeting a friend there so I'm going to brave letting DD loose on some paint!
Bridgewater High school also has a leisure centre which has parent and child sessions, I'm not sure how you'd do that with a 3 year old and a 1 year old though.
I have heard that Marbury is lovely so will add that to our summer to do list. I agree, lots of time outdoors is a good thing. DD has a thing about running at the moment, it's the absolute most fun thing for her.