Whatever your contract says is what notice the parent must provide.
My contract says the deposit will be forfeited if the required length of notice is not given.
Just put everything in writing to this parent to cover your bases, and refer to the contact paragraph that quotes the withdrawal notice requirements, and then let them know that you won’t be returning the deposit.
They can make up whatever story they want, just document everything in writing.
If you are in Ontario, the ministry can pop by whenever they feel like it, and we are required to permit them access to the residence.
Typically they just want to make sure you are following daycare ratios and will document kids names and birth dates. They also want to see your waivers signed by parents if you are running privately.
Don’t panic, if you can prove everything with emails and your documents are in order.