I think, especially as you've said she's a good and reliable pupil, you should make an exception for this case.
You seem close to the family, (or at least I get that impression), and whilst I understand that you will unfortunately not be paid for these lessons, if you can I would be inclined to not even mention it unless prompted by the family.
It's great that she's coming back to lessons so soon, and you might just find that playing and continuing learning with you will be a great way for her to help deal with things, I think we all know of a time when playing has helped us to escape or cope in some way. And, in the long run, your understanding and sensitivity may well keep her playing with you long into the future, giving you rewards as a teacher, and financially too.
You may find in due course, they approach you about the money side of things, once they've had time to settle down a bit and get things organised, and I'm sure that they would appreciate greatly your understanding and waiting for them to come to you, after all lessons are probably the last thing on their minds right now.
I get the impression as a good pupil they won't be wanting to take you for a ride and try and fleece you out of more lessons, but if she's not coping very well or struggling with coming, maybe reducing lesson time/frequency for a while would be useful? That way, they may feel more able to cope with the commitment/payments and keep the slot, you would still have a regular income, albeit slightly less, and there might be less of an issue missing lessons because of this? Even if only for a few months, it could just ease the pressure on both sides? I don't know if that would work, just a suggestion!
As for being "normal", I suspect just playing it by ear as the lesson progresses will be just fine, you certainly sound caring and sensitive in your original post, and I'm sure you will be invaluable in helping keep some normality in the life of a girl who's world has just been turned upside down

I hope things work out ok