OP--coming at this from years of experience as a teacher, GS leader, CS den leader.
I would not accept any new girls into your troop at this time. Think about it over the summer, have some long talks with your co-leader about it. If you don't accept any girls, then you cannot be accused of passing this one girl by in favor of others. You may find that you like a smaller troop and that the dynamics of the smaller troop work better for you.
You have a great troop dynamic at this time. Bringing in a girl who is known to have problems, and especially one who locked your 2.5 year old in a shower in your home (did she have any regrets???), is not something you do lightly or with the guise that "we will let her join and she will she our positive role models and things will magically change." It just doesn't work that way.
As pps have said, you will have her for one hour a week, once a week or every other week depending on when you meet. You will not be working with her one on one, you will be working with many girls. When she misbehaves, how will you handle it? will she accept the redirection or will she cause more problems? Will mom be willing to come and sit with her every week? Is co-leader (since she wants to have her join the troop) willing to be "in-charge" of her during the troop meetings/outings/etc and especially when she misbehaves, sitting with her and missing out on the fun/activities the other girls are doing? I could be wrong, but co-leader's thoughts may change if you present it to her as "you will need to be in charge of her".
Alsom things will not magically change between her and the other girls just because this is scouts and not school. They are in school together, they know her and how she treats them and others. It doesn't end or go away when the bell rings and school is over for the day!
It might be best for this girl to find another activity to join, one that is away from school and those who know her in order to give her a fresh start. That might help her and in a couple of years, maybe your gs troop will be a good fit for her.
Are you willing to have your troop possibly fall apart because of this one girl? Because if she joins and continues her behaviors, the other girls may decide girl scouts isn't any fun anymore and drop out. Or the night you meet "won't work" and other mothers will form their own troop to meet this need. Then where will you be?
It is sad to think that this even has to be discussed, but it does. This girl needs help and that help is not going to be given/received in a one hour troop meeting every week/every other week. i would hope that the school and the counselor are working with her.
citadelle--quote from you
It is difficult for me to express how this kind of exclusion has hurt her. It has been devastating, and nothing she has ever done warrants it. She has never been physically aggressive, ever. She's a little immature for her age, quick to anger, and stubborn. She's difficult, I know that. But she's human, and she wants, needs, to have human connections.
I am sorry your dd is struggling so much. However, she is doing things that alienate her from others; she is not being physical nor is she being a bully. But she is doing some things that are cutting her off from the other girls--immature (comments and behaviors, I would assume), being stubborn, getting angry. This could easily make others not want to be around her. I know that you are struggling with helping her as she doesn't want to hear it from you/have you help her.
It can be hard as a parent to watch this and not be able to help. Is your dd getting any kind of help/therapy to deal with the anger and being stubborn? Sometimes hearing it from an outside source is best and can help her recognize triggers, learn how to deal with them, etc.
I know our school district runs a "help" clinic that is offered to parents with children who are struggling with these same types of issues. does your district offer anything like this? If not, I would definitely look into doing it on your own. You need to get her help now before it becomes worse. Just moving her to another school district won't magically change it unless she gets help with these behaviors and learning how to control them. Good luck!