Unfortunately, the answer to your question is “no”. No one can make another person go to therapy. Even if you did get her to go, you already know from prior experience that you can’t make her take it seriously.
Your father should be protecting you from your mother’s behavior. He is the adult in this situation. Although you are exceptionally mature, you are still only 14 and deserve his protection and support. It’s up to your dad, not you, to confront your mother. It’s up to your dad, not you, to make your home safe. If I were seeing your family, I’d be asking him why he can’t find a way to do that. There may be good but not helpful reasons. He may need some support but that’s not something you can provide. He needs to turn to other adults for that.
Not everyone gets the kind of family they deserve. Unless your father insists that your mother get into therapy with him, things are not likely to change. For that reason, I encourage you to make an alternative “family” for yourself by finding really good friends and who are interested in doing worthwhile things together. Such friends become lifelong supports for each other. You might also find it helpful to go to Al-Ateen meetings.
In a few years, you’ll be able to leave home and to start making a life for yourself. I hope you will find a partner who can join with you in the project of making the family you’ve always wanted.
I wish you well.