Cannon Hall is the other side of the M1 it's nowhere near York and about 45 minutes from Leeds, closer to Wakefield and Barnsley.
Eureka again nowhere near either its in Halifax! Absolute mileage from York.
Having lived in a suberb between Leeds and York for much of my adult life and until oldest was 3 I would suggest:
Stockeld Park - outdoors and really fantastic
Lotherton - outdoors, again great, easy parking, okay food, there's an aviary with penguins, other birds and meerkats etc. Plus parkland an adventure playground and a smaller playground designed more for the littlies. This is near where we lived and very much in between Leeds and York.
Roundhay Park & Tropical World, t world is inside and the park is obviously outside, its lovely parkland, and there's a great playground which was revemped a while back. Quite a walk between that and t world. Cafe is rubbish, the pub is better (fam friendly).
The only soft play I would go to would be Grasshoppers in Tong....I hate soft play but this really is amazing in the context of soft play , nothing else in the area comes anywhere close, it's not at the York side of Leeds though.
Temple Newsham is okay but it's always full of dog 💩💩, literally everywhere and there's always loads of crazy dogs off lead
Where do you both actually live? My favourite places were always A World of Their Own or Newby Hall, the first is Harrogate way. And NH is off the M1 but closer to Ripon than York.