Based on what I know, a TF leaves (dies) if one racks up enough care mistakes. As far as I know, overfeeding does not count. You should be safe.
You can stuff her mouth full of bread, but I don't think she'll leave because of that. (forget to feed her, that's another story.)
Also based on my experience, it will probably take roughly 45 games to work off all that excess weight. Also, every time they "use the bathroom," they shed a couple of pounds.
You said she didn't want to play? What were her Hungry and Happy hearts at when this happened? I've never had a Tama refuse a game.