Well, most rabbits don't like being picked up, so yes, she might try to persuade you to not do it. They can be pigheads, and get grumpy if something is going on against their will.
Is their any way to connect her cage to the playpen, like a cardboard tube or tunnel?
I train them to get used to being picked up, when they let me pet them for some time I sit on the floor and just put them on my lap, give a treat and let them hop away (or let them hop away and give the treat then). When they don't struggle much with that anymore I pick them up, hold and pet them for a second, slowly increasing the time, and let them hop off me, immediatly followed by a treat. Treats, repitition, treats, patience and treats
work.
Treats can be quite small pieces of favorite fruit, herbs, vegetables, small amount of pellets etc. Also stuff sold as treats, as long it's not too much. Keep in mind that new stuff needs to be introduced slowly, starting with fingernail sized pieces.
A thick sweater helps a lot when the rabbit starts biting while holding it - ignore that, if the rabbit learns that biting gets him what he wants it can get difficult. Also, do what you do with confidence. Rabbit doesn't like it? Proceed anyway, if you shy away when she starts a mock attack on you she learns the wrong thing, don't apologize to the rabbit but don't forget a treat afterwards.
At least that's how I do it, there is so much more on the topic, but I follow my intuition and keep it simple.
