I love your cats! The mother looks like one of my cats that went missing 2 years ago.
Watch for the warning signs that she is getting ready to bite when you are petting her. Sometimes for some people, it’s hard to see that your cat is becoming agitated, but if you look carefully and you know your cat, you'll soon figure it out. She could be enjoying being pet for a while, but then a second later she could be kicking and biting your hand. If she starts getting agitated, walk away and leave her alone, or just stop petting her. Cats have boundaries and a set of rules...pet them for too long and consequences occur.
Of course, cats can sometimes just be turds. My cat has a habit of jumping out of bushes (basically appearing out of thin air), flying across the ground, and attacking my feet. It’s all just fun and games for him, but if you take time to get to know your cat you'll soon figure out if she's just playing or being mean. If you want to completely stop the biting, try what other people have suggested. (E.g. the water) However my cat wont bite me as long as I respect him, and when I know he has had enough petting, I will leave him. It does work, my cat will always show me his stomach, because he trusts me.
If your cat just has a habit of running up and biting you, well, that’s a different story. I dont think my cat has ever drawn blood on me by biting, but he has a couple of times with his claws every now and then we he gets too excited...cats are cats. You can also use a stern voice when she goes to bite you, or if you have a sound that you use when she does something wrong, use that. My cat knows that the sound "Pssssst" means he is doing something wrong. Hope you get this sorted out!