Daycare filled our reserved spot despite us paying a deposit which they acknowledged receiving. What to do?

Location: Ohio

My wife and I conceived our child last summer. Knowing how insane daycare waitlists are these days, we began touring places within a week of finding out. Last August, we toured a place and decided to go with them. They required a deposit in the form of a check to reserve the spot (starting in June 2025). I didn't have my checkbook handy so we returned to drop it off the next day. Didn't sign any paperwork at that time.

Fast forward to now, and our child arrives. I call the daycare to let them know and ask if there's anything we need to in advance of our start date. The director seems confused and tells me we're not on the list. I asked her if the deposit was [exact amount], she said yes, and I told her I have a bank statement showing a check was cashed in that amount six days after I dropped it off. She looked back into their files and confirmed that they had indeed received and cashed the check, but apparently written nothing down about us and subsequently gave the spot to another child. It may or may not be important to note that the director was not the employee we worked with the day of the tour.

By now I am panicking because there is no chance in hell we find an alternative day care in time and neither of us can stay home. The director says she is going to try to contact the other parents on the list and see if there are any last minute drop outs, but I'm not holding my breath.

What are my options here, legally? The way I see it, we had a contract and they breached it, so can I force them to kick off the family that signed up after we did? Or have them pay the difference in cost between them and a nanny? Thank you in advance for your help