I'm sorry to hear your children have been bitten.

Currently there are no laws to protect any member of the public when they are bitten on Private property,as this happened in the dog owners garden it's highly unlikely any authority will be interested and they certainly can't force the owner to make a decision on the dog.
Now had this happened in the street you could have reported it for been dangerously out of control in a public place.

I think you would end up taking out a private case,which could be very costly.