OK, not married in Church, so no sacramental marriage – bad. However, mom is a Catholic, keeps in touch with the Church, and has had the kids baptized – good. Dad probably not a Catholic, or a severely lapsed one, and shows no interest in taking care of the kids – very bad.
Harsh though it may sound, I think it’s hopeless as long as the kids are with her. There’s no way she’s going to find the strength to be more strict under the current circumstances, and these kids aren’t going to break out of their nasty habits of their own accord. In other words, the kids have to go somewhere else for a while for a couple months (minimum) of “unspoiling”. Doesn’t your friend have parents, other family, or a friend that can be of help?
Oh, gosh, no, it is not hopeless. We had a poor man in our parish whose wife just up and left him and their children. I had his oldest daughter as a student in religious ed; I think she was 2nd or 3rd grade at the time. All of a sudden, she went from being quite well-behaved to acting out in class and just a different kid. Just an utter pill. Luckily, the change was so puzzling that I just rolled with it and then later asked the director of religious education about it, who filled me in on the situation. Aha! OK, we know this girl is only trying to cope with having the rug pulled out; she wants to “do something” about her situation, but has not idea what to do. I put the boundaries on her, but I also paid attention to her in positive ways and I was more “oops, we can do better than that” on the firm boundaries than “hey, cut it out!”
Fast-forward about a dozen years, and his children are in high school and college. He did a great job. The OP’s friend can get through this and she can have a great relationship with her children as their parent. She isn’t alone; she has people who care about her around her. It won’t be easy, but she is not alone and she and her girls can make it.
As for having no sacramental marriage, yes it is bad but now that it turns out her husband abandoned her at least this poor woman wasn’t abandoned from a valid marriage and could perhaps find a real husband to be a father to her children and bring them up in a real and lasting marriage.
It is too soon for that, though. For right now, she’s probably looking at behavior that is a child’s response to feeling things are out of control. The more the mother brings order and serenity to the household, the more this behavior is likely to die out, as opposed to difficult behavior that has an organic cause that will have to be managed for the child’s entire childhood. This could get better a lot sooner than that and with less professional intervention than that. It will be rough at first, but when the mother believes in herself, has support and direction, and uses that to regain control and supply the children with stable guidance, the children will come to accept it and be far happier with it. They’ll still have all the bumps and storms of childhood to go through, she’ll have the issue of how to compensate for the lack of a father and husband in the home, but it can be done.