My female cat keeps getting bullied by her brother

[SleepyCat]

Belle and Zeus used to get along better when they were kittens but now Zeus chases after her a lot. He often approaches her and bites the back of her neck. Sometimes he'll just sniff her, and she immediately turns and walks away and hisses when he gets close. Is this a dominance issue? I want them to get along better but I am not sure how to do it. Belle also has a strange tendency to walk away when we try to pet her, but rubs against surfaces with her tail up right after. It confuses me. She meows and seems like she wants us to pet her but then walks away.
Any suggestions would be appreciated.

 

[linda2147]

is she spayed? and is he neutered? The grabbing of the neck is a sign he wants to mate, even if he is neutered he still has a nose. Get a squirt bottle and everytime he stars after her give him a squirt and he'll run away, may have to do this more than once but eventually he'll learn.

As far as her not wanted to be picked up that is normal, if she wants to sit with you she will jump in your lap. a lot of cats just don't want to be picked up. Nothing unusual

 

[SleepyCat]

They are both neutered. Thank you!