I think donating spares to the centre is a great idea, if they've need of them. I know I've been caught out without sufficient spares, too, and have appreciated the loaners.
Then the centre will be reminding the mother directly to a) send spares and b) return the stuff that's been loaned to her, and it's no longer on you.
It's very nice of you to think of the little girl, though, good on you.