The biggest mistake I see that was made is that both coaches left the field before all their players were picked up.
Clearly you've had your hands full with this young lady for some time, and she's given you every reason to leave her behind. However, you knew that when you posted her story and your dilemma, which leads me to believe you know you can't just walk away from her. That speaks volumes about you, and for that I tip my hat to you. It seems to me what is missing is unwavering ground rules with real consequences. Once you and your assistants have defined exactly what you expect, and are willing to enforce no matter what happens, then two conversations need to happen. First, you and the young lady's mother need to have a candid conversation where you tell her of your concerns, and new rules/consequences going forward. You also need to verbalize your wish to have a positive and lasting influence on her daughter through the great game of softball. If the mother agrees with all rules and consequences, then you need to have an honest and firm discussion with the young lady that includes all the rules/consequences in addition to you verbalizing your genuine belief in her. If either mom or daughter can't live with the rules, I would walk. If they agree by signing your rules/agreement, I would allow her to earn a position on your travel roster.
We're never given more than we can handle, and I believe you are being called to have a positive impact on this young woman at a very critical point in her life. It sounds as if she is desperately looking for structure and "normalcy" in her life. If the team doesn't provide what she needs, she will find it elsewhere.
I'm willing to bet you'll be back here in a year or two telling us about the achievement of an amazing group of young women, and the leadership that one particular young lady has shown over that time..... Good luck coach.