I'm a 15 year old member of the church. My father has gone into drugs and adulterous relationships. My mother promised me that she would get a divorce and that she thought it was best. I have prayed and studied about this matter for literally weeks. My father has now tried to return to our home as if nothing happened and my mother let him back in at the snap of his fingers. Now she acts as if she isn't going to go though with the divorce. I've ranted long enough, so I must ask how do I convince her to continue with the divorce?
While the answer is clear to you, your mother is having a hard time because this is the man she chose as her lifetime companion. She is hoping against hope that this time he might change. While it seems clear that he has no desire to change, your mother has to fully convince herself that she has lost the man she dearly loves and many people have a hard time with coming to a permanent decision about such things. I suspect she thinks that if she divorces him, then there will no longer be a restraint on his actions and he will get even worse.
You see things differently. Odds are that you are probably right. However, you can't make someone to the right thing. This is why you've been losing your cool and arguing with your mother. You are trying to force her into a decision she doesn't want to face. Angry usually arises when you are attempting to make something happen, which you really don't have control over.
You've made your case. You need to be satisfied that you've done your best. However, the actual decision is your mother's. What you can do is make sure you and your siblings stay safe and are not influenced by your dad's drug use or sexual sins.
If you ever need someone to talk to, about anything at all, you are welcome to contact me. I'll do my best to help, even if it is just listening to what is happening in your life.