So your DD was pushing your cat down and screaming at it? And your cat only scratched her? I would say give the cat a medal.

Any animal (including humans) will only take so much antagonism before they will defend themselves. In all probability the cat was giving lots of warning signals before lashing out. Many cats would have bitten in that situation. Children need to be taught about pet safety and it is absolutely unfair to expect a cat or dog to just take whatever it is given by children. This is a very predictable outcome to the situation and can easily be managed by giving the cat areas it can go to get away from the kids, and by training the children what is and isn't appropriate behaviour around animals. And if you find your children just aren't old enough to know what is and isn't appropriate behaviour then to only allow access to the pets when supervised. Good luck with your DH!