Daughter can't be allowed to call the shots. If OP's friend gives in she will have lost her husband (whom we can assume she loves) and will be other own with three children 2 toddlers and a demanding teenager.
I think this is just a young girl who has been used to having her own way and ruling the roost with a mother who was too afraid/ exhausted/ depressed/ guilty to discipline her.
She may well have been jealous and resentful whether mother re-married - especially when her babies arrived and attention was taken from her onto these little ones. Couple that with stricter environment, and the natural bloody-mindedness of the teenage girl, ands is desperately trying to assert herself again and bully her mother.
It won't do anyone involved any good to give in to her. There is not just one child to think about here, there are three.
Someone said said the husband "doesn't sound very nice". Why not? Because he won't be bullied by a child? Because he likes good manners and a disciplined routine for his children? Because he isn't prepared to let her do what she likes, when she likes and with whom she likes?
Giving in to a child is not good for them, especially if it is giving in to bullying behaviour. It must be terribly hard for OP's friend, but if she can, as someone else said, keep open bot her door and her routes of communication, then things, will, I am sure, work out.
The girl is safe with a cousin, she isn't sleeping on the streets. And it strikes me that she sounds someone who, if she had been abused, wouldn't waste a moment accusing her Step-dad. I don't doubt the poor girl has problems, but letting her have her own way in everything won't help her cope with them.