Monkey World? also at Trentham.
Cheadle is close to Cheshire so you could be at Stockley Farm in about 40 mins, or the Wheelock Farm shop which has a gorgeous play area with ride ons and its only £1.
Blue Planet is over at Ellesmere Port and will take about an hours drive but is great for toddlers and has a little outdoor play area and an area where kids can stroke the fish.
Gullivers World at Warrington, very easy to get to.
Tatton Park has Home Farm, wonderful play areas, (though a lot of it is aimed at over two years), brilliant gardens, and midweek you will have the place to yourselves.
Viewing area at Manchester airport used to fascinate my toddlers!
If you head over to Derbyshire the Heights of Abraham is pretty impressive with a cable car ride over the main road and lots of caves to explore.
Hope you have a lovely time.