You have to give her a few weeks to settle in. You just took her from her home and plopped her in a whole new unfamiliar place with unfamiliar people walking around, it's understandable that she'd be skittish and afraid. Give her 3 days locked in her cage, them give her 5 days to wander around your daughter's room with the door closed, then gradually give her more and more space so she can slowly get used to her new home. I'd recommend you do lots of sitting down spending time with her, letting her approach you on her own terms, so she learns that you are not threatening. Humans standing up are much scarier than humans closer to the ground! When my bunnies were new the only way I could approach them without them running away was crawling on all fours.
Also, at 5 months old she is undergoing puberty, and this tends to make bunnies more aggressive and unfriendly than usual. It's the perfect time to take her in for a spay. There are many good reasons for spaying bunnies and it's highly recommended.
Most rabbits hate being picked up, and always will. They are prey animals, so when they are picked up their instinct to struggle to avoid being eaten kicks in. You can't really train a rabbit to be docile about it, you have to train yourself to be quick and firm. We have a 5 year old who can pick up and hold the rabbits much more easily than I can. This is because young kids don't really grasp the concept of being gentle to others, and they often grab the rabbit up in bad positions and hold them so tight that they are too much in pain to struggle. This is what I suspect the 3 year old has been doing.
Your 10 year old, along with the rest of us, is probably much more mindful of hurting the bunny, so we are softer in grip, which allows the bunny to wiggle her way out. It's tricky to learn to be kind to the bunny while at the same time holding her firmly, but practice makes perfect! There are many ways to hold a bun, but here's what I do:
Sit on the floor and pet the bunny for a while so she is calm. Position yourself behind her, and firmly grasp her caging your fingers around her chest and neck area, making it so that she cannot leap forward, which is the first thing she will try to do. When she realises her front legs are caught in your finger cage and she can't move forward, she will then try to wiggle out backwards, towards you. This is when you quickly remove your left hand and swoop it under her tail. With one hand supporting her chest and the other supporting her bum, lift her up quickly!
Hold her firmly to your chest this way, upright and fully supported. When you want to let her down, don't just extend your arms down like you're putting down an object. She will start struggling when she sees the floor. Holding her to your chest, sit down on the floor, lower her into her lap and let her hop off.
I'm sure there are many other members who recommend different ways of holding your bun, but this is my scaredy-cat method! I used to be very afraid of hurting bunny and getting scratched or bitten myself, until I figured out this way to hold them. I hope it works for you and your daughter.