First of all, I think it was really great of you to take your department out for a Holiday lunch. A supervisor is in NO way obligated to spend his/her own money on work subordinates. It is too bad that Jill ruined it for the rest of them (but I agree with your stand on this luncheon).
I am also a manager, but in a different kind of setting. The conversation you stated that happened with Jill should not have gone that far at all. She has no business "hinting" or asking you to foot the bill for a department X-mas lunch. My reply would have been something along the lines of, "Jill, it's time for you to get back to work. Please do not bring this up again, the issue is closed. However, if you do bring this up again, I will be documenting it in your employee file and speaking to HR." Then I would document that you had told her in no uncertain terms the issue was closed. That way, you would have written documentation of both of the conversations on the issue as fodder for HR to finally do something about this person.
You are her manager, not her mother, for goodness sake!