Hi welcome to YT and thank you and your family for taking in Lucy. If she is 2 years old and a rescue, then you are probably right..she probably wasn't treated the best by her previous owners.
The Bonding thing - I could say to have your daughter do ALL the caretaking for her, but to be honest...that doesn't really seem to matter. I have 2 dogs. I do everything for them except on rare occassions when my husband is off work due to weather or between jobs..then he is home by himself with them. Anyway, my older and male dog is up under me 24/7. He is a complete Mama's Boy. Mandie, my 7 month female yorkie, bonded with my hubby from minute 1. I take care of her just like my boy, but she is a complete Daddy's Girl. My hubby doesn't treat either dog different..that's just who they decided was their "person" (as stated above). I don't think there is much the person can do about it, to be honest. I've accepted the fact that my Mandie (the dog I wanted for 20 years and finally got) is just closer to my hubby. It is what it is.
Going Out - you really don't have to take her out so many times a day unless you just like going out. Mine can go all day when I'm at work or when I'm at home..we go out a lot because I'm doing stuff out there and they love playing outside. No need to crate train.
Discipline - I was once told not to treat a dog based on it's past. I will say that Yorkies are totally more sensitive than any other breed I've had. So, don't yell at her...just use a firm No. My only suggestion is to work with her learning obedience commands with praise and treats. Work with her to learn sit and down and make it happy. Then when you say it, eventually, she'll do it without the treats but not cower..she'll have happy things associated in her mind with those commands
