Doc - if the shoe was on the other foot and you needed to work with your sponsor on Saturdays how do you think she would react? Also, is her working with her sponsor really going to take up the whole day?
If that is the only day that her sponsor will meet with her and it is important to her then I don't think it is that unreasonable of a request. It would be completely different in my mind if her sponsor would meet with her on other days, but she choose Saturday against your wishes. Could you get a babysitter to watch the kids on Saturday while she is gone if you need the day to yourself?