Oh dear... I am so very sorry for your loss.
I personally would close for the week and let the parents know that they should also be prepared to have back up care for the following week as well and you will keep them in the loop. I allot myself 5 paid personal days each year - and I pay a portion of my daily fee back to parents if I run out of days. In a case like this, we have savings that would allow me to close for considerable period of time without being financially affected, but I realize that isn't the case for everyone.
That said, I would absolutely close for the week and see how you're feeling over the weekend.
Again, I am incredibly sorry for your loss. My family's thoughts are with you and yours.