Really recommend visiting this country park, either with the family or for just a chilled walk to clear your head, the 3.5 mile loop round Strathclyde Loch would meet your needs.
Accessible Parking ✅
Accessible Toilet ✅
Play Park ✅
Accessible Equipment in Play Park ❌
Cafe (Tearoom) ✅
There are a number of car-parks to choose from so I very much doubt you'll have any difficulty finding a suitable space. In the main building there is a cafe and toilets - including an accessible one.
Next to the beach area at the loch there is a playpark for children. There is no accessible play equipment that I could see.
Video coming soon.