I could think of several reasons why your anger is being directed at your mother. Most of this is somewhat speculative, but I have been in a similar scenario with my mother at a time in my life, so hopefully it will give you something to think about at least.
Your father doesn't sound like a great guy. Your description paints him as abusive and irresponsible. You know this, and recognize this. But you must reconcile with the fact that you still love him, which will cause dissonance in your mind. Put a pin in that thought for a second.
You say that your father was abusive towards your mother, but did not indicate that he directed the abuse upon you or your siblings. Over years of seeing this as a child, what conclusions did you draw from this? If your father was out of control and just violent, then why were you not subject to his abuse as well? How do you justify his actions in your mind (the mind of a child, over years of witnessing this)? Maybe you end up believing that your mother deserves this, or maybe you believe that she is too weak to stand up and defend herself, and her perceived weakness becomes disgusting to you. This is not something that has to happen on a conscious level. This is your subconscious trying to protect you from the dissonance of loving your father, and witnessing him commit these acts.
It sounds like your mother initiated the divorce. Which, in a way, means she has taken your father away from you. You loved your father and she intentionally took an action to take him away. On top of that, you are now left as the eldest son, at 16, perhaps with the rational internal expectation that you now have to step up and be a man, and a replacement father for your younger siblings, a position that you are not ready for, and perhaps resentful of. Again, you can trace this back to your mother's decision to get this divorce.
Let's also look at your mother and father again. Your mother is working hard to make ends meet, while your father hasn't worked in years. Your mother is who you view as the responsible one, while your father is viewed as irresponsible. So all the anger that you feel, it is natural for you to lay that at the feet of the parent that you view as being responsible, while letting the irresponsible one off, because that is how you have come to see your parents.
Also, you most likely intrinsically identify with your father. It is easy for you to imagine yourself in your father's shoes, but not your mother's.
These may or may not capture your feelings, but I would imagine some of it is close. By asking this question, you demonstrate that you understand that these feelings are not quite appropriate or rational, which probably causes even more dissonance. But, thinking about the why is the key to you getting to the point of understanding your mother and not blaming her. When you have these feelings about her, write them down in the moment, unfiltered and read them back. Try to focus on why, even if it makes you confront a thought that you don't want to admit that you have. Focus on what makes you resent her, and pull those thoughts apart with logic until they can no longer stand on their own. This probably will not be easy. Seeing your mother go through abuse for years, especially if you were not subjected to this same abuse, has likely tainted your view of her, and made it much harder for you to identify with her, but it sounds like you know that your feelings about this are not rational, and you need to work through them. Seeing a therapist about this would be ideal, as they can help you deconstruct your feelings around this and work through them.