Hmmm. I think the vacation pay issue is a bit tricky and depends upon if any specifics were discussed and how vacation has been informally handled to his point.
1) Since you agreed on 4 weeks notice, I would put it to her this way: "I'm sure you understand that our circumstances no longer allow us to spend money on a nanny, so we cannot use you for 6 weeks. We originally agreed on 4 weeks and are happy to have you stay for 4 more weeks. However, we would be grateful if you chose to leave sooner, considering our situation."
2A) If you did not agree to accrual of vacation days (nothing of the sort has ever been discussed...and you have never hinted or executed any accrual) I might consider the following: "I'm sorry for any confusion, but your employment agreement included vacation days to be offered on a monthly basis. Vacation days are not accrued and not stored-up or paid out." Then, I think you have two choices. (1) You leave it at that and don't pay her -- and expect some disagreement and resentment, or (2) tell her, "Although our circumstances really don't allow this, we want to offer you 3 additional days (or whatever) of pay.
2B) If you did have some agreement about vacation accrual, I would tell her that she is going to have to use the remaining vacation days immediately, during these last 4 weeks, and there will be no vacation days honored after the 4 weeks. You have to pay her for 4 weeks anyway, so let her take them during those 4 weeks.
Let us know how you handled this and how everything turned out. Best of luck!