I don't know the details of why you decided to put down the lab/border collie cross who bit your daughter. Some dogs with working dog instincts can demonstrate 'nipping' or 'biting' to herd. Those who show this often direct it at children & may not be suitable to have as pets with children. If this applied in your case, I wonder if you got advice about possible rehoming of the dog in another sort of environment...before you decided to have the dog put down?