JRT Just Bit My Daughter

Our JRT just bit our daughter's arm during an encounter with our cat. The cat pushed the door open and came into the room and the battle started. I was trying to get the cat, and my daughter was trying to get the dog. When she reached for his collar to pull him away, he bit her arm.

From reading about JRT, I know they have a hunting instinct, but not sure if I am comfortable with the bite. Or if any dog would have reacted this way.

He is a rescue dog and we are in week two of rescuing him. He has shown tons of progress except with our cats. He stopped peeing in the house, barks a lot less, is started to eat hard dog food and now walks beautifully on a leash.

Any suggestions, ideas or comments.