Whew --- sorry you have to go through all this.
My immediate thought, with regard to your last sentence, is: Ask your psychologist to step in. I know that seems radical but I think if he/she can talk with your dad, maybe they can figure out something that will help you get some moments of "down time" from the stress.
I give you credit for locking yourself in your room rather than lashing out at your mother.
I'm not taking your dad's side here, but I want to point out that he obviously cares about you, and told you to call him at work whenever you need to (which is more than many parents would do). He is probably very stressed out, worrying about you, your mom, his job, and other stuff.
At the same time, though, he IS a parent and it sounds like he's struggling to manage the situation.
Do you have an aunt, uncle, or grandparent who could help out?
Again, please try to ride out this chaotic time and see if your psychologist can work something out with your dad...
