I'm so sorry about your Nan and about your mum - sounds like you're going through an awful time 
Your "DP" sounds just vile. You shouldn't have to put up with this shit. Getting rid of him sounds like the best course of action.
My gran had a stroke whilst she was visiting us and was hospitalised. It was immediately apparent that it was pretty serious. We all got to the hospital, and my sister's "DP", instead of showing any form of support, sat there on his own, in the corner of the room, playing with a jigsaw. He was 30 at the time.
He also threw a strop if things didn't go his way. They were engaged, had a house together, dogs, and had been together for about 5 years.
For her, that was a turning point. She got rid of him 4 months later.
She is now happily married to my DBil who she met a very short time later. She has never been so happy, and she tells me that it highlights just how shit her previous relationship was.
You don't have to put up with shit like this from anyone, especially when it is so clear that you need support, not arguments. He's telling you who he is - please listen x