She most likely trusts you with her child but she may have had a bad financial experience in the past and is now cautious.

Honestly, I'd want the cheque back too if it were me. I think the safest way to avoid financial issues is to have complete control over your money. I would have had all their cheques ready for exchange to avoid any issues.

I'm sure it will all be fine We sometimes mistake people's ways to keep themselves safe as mistrust towards us specifically when it's just not the case. ( I mean this in all aspects of life not necessarily just daycare)