Well, I personally don't like to get into such discussions on the internet, people could be inconsiderate or simply give suggestions without knowing what is the outcome of their comments. I'll however try and tell you what you should be doing in your current state, and hopefully my answer is a good one that would satisfy you.
I've read once in a book that the better thinking process you're able to process the better results you're able to achieve. In your case, i believe you're asking the wrong questions - and hence reaching a dead end in your thoughts. I'd recommend writing your thoughts on a sheet of paper, each and every though you have about your parents and your current situation; highest priority to lowest priority: as in things you should resolve first and most importantly should be on top of your list. Then you try and think of what you should be doing in order to fix what is going on in your life at the moment, feeling weak or getting emotional about a certain situation is part of growing up and getting stronger sense of survival - your brain will start unconsciously thinking of ways for you to overcome your struggle. Having a divorced parents could be tough i can only imagine, but it is not something you must attach yourself to, you're a strong man who can handle things on his own and fix his own life without having to rely on others - whether it was your mother or your father. I'd suggest you reach out to your father and try to fix your relationship with him, tell him how you feel about this situation and tell him you're no longer a kid who doesn't know anything. There is no father in this world who wouldn't be happy to hear his own son speaking like an adult.
I'd also recommend you stop thinking in negative perspective, questions such as "Why can't a divorced parents have a healthy relationship after divorce?" or something similar won't fix your problems, It'll only burden you and prevent you from enjoying the moment - what is in-front of you, in that case, your father. If you're living with your father, and your mother is busy with his work or whatever, then your next goal is to fix your relationship with your father, once that is done, give your mother a call, tell her how you feel about his, and what are her plans for you and your sister, tell her not to keep you in the dark.
I honestly I'm not psychologist, and I know little about how to fix such issues. I tried to be reasonable in my reply and hopefully you get something out of.
DA Administrator of the year 2012, 2014 l DA Artist of the Year 2012, 2014, 2015 l ~Lead, follow, or get out the way~