For a cheap morning both odeons do kids showings every weekday morning; Braehead at 11:00 and the quay 10:30 of an older film which is only £2.50 per child and adults free. Different film each week.
The glasshouse at Queen's park has lots of bugs, reptiles, fish etc and also has a summer holiday program and a small soft play area (was shut down but open again now as far as I know) A good one for getting in the park but having the inside option if the rain appears.
The Burrell collection in Pollok park is free, though may not have too many things to hold their interest. You can see the heilan coos from the car and again get in the playpark if it's not too wet!
The museum of modern art in town isn't all suitable but the big hall downstairs has brightly coloured ones and normally some free kids activities in the holidays.
Scotland Street school museum is also free and right across from Shield's road underground so you can use the 2 kids travel free with an adult offer to make it quite the day trip!
The police museum is free too though I haven't been but hear it's not too big but good. Not sure how suitable for your ages though.
Pets at home at Linwood is good to have a wander round to see the fish and rabbits etc though won't kill much time!
All the libraries do summer holiday things, normally twice a week, where they do a story then an arts n crafts type thing. Whole foods in Giffnock is doing free kids story telling on Fridays too.
Best thing to do is buy all in one suits and wellies and get out to the parks etc at any break in the rain!
You can then also do things like Barshaw park, whitelee wind farm etc on a drizzly day and just not worry about it too much.
Will post more as/when they come to me.