Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this concern about Mitzie. Her behavior certainly sounds quite puzzling, doesn't it?
I have to wonder if she's already come into heat, given her age, which might account for her behavior. Most cats become more loving when their female hormones are present but other cats can behave just the opposite....or at least a few I've seen in my career.
If this is the case, then once she's fixed, she may become the friendly cat she once was to other members of the household.
It's also possible that she's associating some sort of negative trauma or event with other members of the family so that she no longer wants to have anything to do with anyone whom she doesn't trust...which would be your parents.
Or she could be one of those cats that I call Jekyll and Hyde cats....they tend to be somewhat unpredictable in terms of their reactions to others in the family.
I tend to advise that these cats be left alone; that no attempts to be made to pet them or interact with them since it may trigger the negative behavior. Basically, just ignore them. I know this may be difficult to do but we can't make these cats be anyone than who they are.
What may also be helpful would be a Feliway diffuser which is plugged into the wall. This is a natural pheromone which was specifically designed to reduce anxiety and stress in cats. It doesn't work for every individual cat but may help reduce Mitzie's reactivity level.
It's often available at local pet/grain stores or can be purchased online.
I hope this helps and is just a hormonal issue so that she's a cat who's pleasant to be around for family members other than your parents. Deb