Wow, I think you dodged a bullet. Always remember that in any stage of the interview process you find yourself questioning anything that it is better to move on to another family. If you start out with worries it usually only gets worse. I've been in both situations, clients who got worse and I had to terminate and clients who learned that they must stick to my contract and I am fair but tough about my business. It's so difficult to know what kind of client you are taking on, but watch for all the red flags and go with your gut and observe parents and children very, very carefully as you interview.
I like to interview after daycare hours so I can really observe the family then set up a playdate before the contract is signed during daycare hours so I can observe the Mom and baby around the other children. Both of these situations give me a great idea of how things will go. If you see the red flags pop up then ask about them and get straight answers. If you see too many red flags you will know it and say no.
In your case clover, I wouldn't even write back to this family, just cross them off your list.