I think your answer was fine. I also stress that it plainly sets out guidelines for both them and me so everybody knows what to expect when certain situations arise.
I had one family sign on and after being with me for three years, the dad argued with me about a policy and got quite rude with me. I told him if he needed to leave and that if he ever spoke to me that way again I would terminate them immediately. Talked to the mom the next day and she told me that he never understood or took the contract seriously. My contract now states that if you agree to sign you are saying that you understand the need for a contract, if you don't understand, don't sign, this is not the daycare for you.