Nuance is the right word, Latin! Not much-- it depends much more on tone of voice and situation than on word choice.
I have just tried rolling them both around in my mind, and pinpoint nothing. Sometimes one sounds a bit more exasperated than the other, but which one?n Maybe 'won't you' shows a little impatience, but it's not consistent-- it depends on actually hearing them spoken in
is overly formal for a situation asking about playing. The likelihood that a child would ever use it is minimal. "okay" is commonly used as a tag in everyday speech for some instances.