I'm sorry your D is hurting...I'm sorry you are hurting.
I don't see anything wrong with reminding your D that she has choices. You don't need to belabor it or put down her mom...but, maybe just remind her that she can choose the school that fits best for her. Part of becoming a grown up is learning how to make decisions that work for YOU.
When things feel bleak, it always helps me to know that I have choices. The choices don't have to be huge...but, just to realize that I do have some control and I can take some sort of action to improve my situation.
Maybe, ask her, "So, you don't like this school. What do you want to do about this situation? Do you want to give this another month? Switch over to the other school? Join some group or something to make friends?"
You may be surprised at the great ideas she has herself. As long as you focus on the fact she CAN handle this...as opposed to her being a victim in all of this...she will feel empowered to improve her circumstances. And, that is a HUGE lesson to learn in life.
If this girl is living with a woman who was suicidal 9 months ago, she will NEED to learn some good coping skills...she needs to understand she is NOT responsible for her mom's happiness. IF D would be happier in another school, empower her to make some decisions for herself. Sounds like she feels really torn about hurting your wife...and, if she was suicidal...that makes a lot of sense...what kid wants to feel like she may be responsible for sending her mom into a vortex of despair? Sounds like she could use another set of objective ears...a counselor?
"You know, it's times like these when I realize what a superhero I am." Tony Stark/Iron Man
“Focus on what you can do, then do it with all your heart.” Lois Wilson