Many rabbits just don't like to be picked up. Remember, in the wild, the only time rabbits get picked up are in the jaws of predators! This just isn't something they're naturally adapted to, so many rabbits just absolutely hate it, and there's not much you can do about it. If she knows that you always pick her up whenever you come near, that might explain why she's scared of you.
With Flash, I know he hates being picked up. I pick him up once per day just to get him used to it and to check his neutering scar, but that's been over 2 weeks so it's mostly healed now. But that's it for picking him up. Mostly, I interact with him by getting down on the floor and petting him, or playing with him.
I also never force him into or out of his cage. When it's play time, I open the door, and he can come out if he wants, but he doesn't have to. When it's time for him to go back in, I lure him into the cage with a treat. He's gotten so used to this that I just have to rattle the treat bag, and he runs for the cage and waits for me to give him one.
Actually, the whole indoor/outdoor thing with having to be picked up to come in might be part of the cause of her unfriendliness. If you were to let her live indoors, where she could just wander in and out of her cage without having to get picked up, she would probably be much happier with you and your family.
One other thing - get her spayed. Even if she's never going to be with a male bunny, female rabbits have VERY high rates of cancer in the uterus. Besides, her personality might become less territorial if she's spayed. That's the case with many rabbits.