Hello and Welcome! Congrats to you and your Too!
My male U2 is about seven. When he came to me (third home as well) he would run up my arm because he had been allowed to in his previous homes. In fact, the only times his former owners let him out of his cage at all, they grabbed him off his perch, hugged him like he was a new puppy and returned him to his cage, usually to show off in front of guests. It resulted in a frustrated bird that screamed his head off. He has learned to play happily by himself now. He was terrified to leave the safety of his cage, now he waits by the door. He still loves hugs, but no longer expects to be held when he's out of his cage. At first, he would wave his foot to be picked up, I would pick him up and reward him with a neck scratch or a small treat. When he would head for my shoulder, I would place my free hand on my arm beside his feet and gently tell him no. We worked on it every day and after about a week and a half he understood shoulders were off limits and no longer tried. Months later and I've recently started allowing Popeye on my shoulder with no problems at all, but that's a personal choice. All birds are different, especially older ones, please be cautious until you know your bird and can predict her behavior. When U2's don't get their way, they can get confrontational, and they will test the limits. Cockatoos are intelligent and emotional, but if you give them companionship and training they can be excellent family members.
My cockatoo was given up twice for screaming.

Cockatoos scream for different reasons, if you can figure out the reasons, you are better equipped to help your bird stop screaming. Popeye likes to tell a few times in the morning and again in the evening. It's normal flock calling and it makes him happy. If I leave and return, he welcomes me home with happy yells, bounces, and wing flaps, my other birds and both my dogs are overjoyed and they make a lot of noise too, that's fine, I usually get loud with them for a few minutes. Occasionally Popeye yells for attention, we completely ignore him and most of the time he stops after a couple of screams. He rarely persists, when he does, we return him to his cage, if he still persists we cover his cage, that works quickly and without fail, when he's been quiet for five to ten minutes, we uncover his cage, five to ten minutes of silence later he's allowed to come back out. There are many training methods, not all of them work with all birds. The best advice is to get to know your bird and build some trust. Believe me it's so worth it.
If your bird is comfortable going from room to room with you and isn't afraid of the shower you can get a shower perch and bathe away. Popeye had never had that experience, he used his giant water dish, slapped all the water out of his bowl and yelled for more. I also gave him mist baths which he loved. The bathroom shower took months but being out of his cage was a brand new experience for him and may not be an issue for your girl. Popeye gets a bath at least every other day, one way or another, it keeps his feathers in good shape and cuts down on dust.
I hope that helps a little. Best of luck. We would love to see photos of your baby girl. What's her name?