My sweet little girl HollyJo is a sweetheart to me, and indifferent to most other people, but she goes out of her way to bite and claw my sister, and m y sister´s cat is the same way with me. I don´t know how to discourage Holly from doing this to my sister and how to stop my sister´s cat from doing it to me. Any advice?

Do you all live together and share a space? Or is this just when visiting one another? If you are living together, it could be jealousy - your cats both sense the bond you, as sisters, have with each other. They could be trying to show each of you who´s the boss.

If you live apart and this happens when you´re hanging out in each others places, it could be the scent of the other cat on your clothing they don´t like. Try bringing something with HollyJo´s scent on it to leave at your sisters house, and vise versa - and change them around frequently so they get used to each other´s smell when you and your sister aren´t there. That way they don´t necessarily associate the "other" cats scent with each of you specifically.

I suspect you have to resist any temptation to scold or punish either cat, and go out of your way to make friends. If you´re at each other´s places a lot, try timing it so that you´re responsible for feeding your sisters cat, and she has to give HollyJo her dinner. It might help if they´re REALLY hungry, so serving up dinner a little later than usual. Have their favourite treats with you and give them lots of treats along praise for behaving. Engage them in play - maybe you could start a game with HollyJo´s favourite toy and hand it off to your sister (feather wands and other interactive toys are good for that). If either cat has a favourite activity (like brushing) work your way towards being the one to give them that attention.

If the biting and attacking is inflicting injury, you could try dissuading it by using the water spritzer to the butt, or shaking a loud can of pennies so the attacking becomes unpleasant. Along with positive attention and praise (and plenty of treats) it might help. Good luck!