Lovely place to be staying mate, can easily waste a day in Greenwich. The park is well worth exploring, it is massive, plenty of shops nearby that will sell footballs etc so could have a kick about. Obviously have the Greenwich Observatory, which might well be too much for a young child, but the building itself should capture their imagination. If not there is always an ice cream van across from it.
Greenwich Market is excellent, some lovely food. Can fully recommend Ruby's Of London, usually Ruby running it, comes across as a French twat, but those cakes are worth her insufferable shite.
Trying to think of a play park, but nothing comes to mind, could well be something in Greenwich Park though.
From the market you can always hop on the DLR and go up to the likes of Heron Quays, walk to Canary Wharf and get a tube to London Bridge etc.