Struggling and Need Advice

My stepdaughter has lived with us since she was about 6 and she’s a teenager now. Her mother uses drugs on and off and drinks daily, but is functioning (has kept the same job working with the elderly for at least 15 years.) She’s got other kids, one lives with her, and has had multiple DCF cases over the years, but nothings come of any of them. I’ve always had a good relationship with my SD. She been very difficult since she was a child though, lying, stealing, bullying, etc. I put in all the work with discipline, as well as the fun, motherly stuff. Her dad never wanted to deal with her behaviors and just thought she’d get better on her own as she got older. Now, after claiming for years how much she hates her mom and her mom’s boyfriend, she wants to move in with them. She doesn’t like that we’re semi-strict. We use parental control apps to monitor her phone, and don’t let her do everything she wants. Now that she’s a teen she wants to have sex, do drugs, go wherever she wants. She says she has no friends here (they found out what she was saying behind their backs), but she struggles making long term friends anywhere because of her behavior. I’ve tried to explain to her for years that how you treat people is important, but she’s doesn’t listen. It’s not even the part about her wanting to live with her mom that’s bothering me, I know it’s normal for kids to want a bond with their parents (even when they’re not so great). My biggest issue is that as soon as she decided she wants to be there, it’s like no one in this house matters. She didn’t care about her father’s birthday or her stepsisters, and she’s saying really hurtful things about us to anyone who’ll listen. She is constantly telling her mom every little thing that happens here, knowing full well her mother will start calling, texting, swearing and threatening over anything. I just can’t wrap my head around us protecting her from her mother’s rage and unstableness all of these years (it was directed at SD a lot), and now she’s using it against us. Her mother’s motivation for wanting custody all of a sudden is most likely financial. They’re struggling and she’s realized she could get a good payday with child support, even though she’s done nothing to help with SD’s expenses over the years. Sorry for the long vent/rant but I’m at a loss. It’s making our home life extremely uncomfortable and unhappy. Does anyone have any advice on a teen like this? Would it be horrible of us to let her go live with her mom, knowing she’ll let her do whatever she wants?