Christmas is over and you did your bit trying to help everyone. Grief affects everyone differently and you are also grieving your mum.
You have siblings. You can and should share the strain.
I think your DH did exactly the right thing at the time by gettting out of the situation and that probably prevented an even worse blow up. So in a way I would forgive him for that. Its worth having a chat with him when its all calmed down, its a two way thing - you can understand how he found it so hard, but now its all over a bit of support/TLC wouldn't come amiss.
Your Dad is grieving and you feel a lot of sympathy for him.
However, that doesnt stop him being a very difficult, rude person, who has been abusive in the past.
You are taking on all his burdens on your own shoulders. OK so he doesn't like the hospital, he has a grudge against the GP for various reasons. So he is making a stand by refusing medical treatment which he needs. You cannot make his misery make you ill.
Can you ask advice from someone like Age Concern for ways to help him. He sounds like he is struggling mentally. You can take some practical steps without taking on all the guilt that your Dad is creating. Eg.. a way of getting him seen by a GP and also some treatment for his mental issues.
There's no point everyone wringing their hands and saying I told him to go to the Dr but he said no, but a, b, c... He is at the stage where he doesn't want to deal with any of it and doesn't care if it descends into chaos.. So find a practical solution - he's not going to make any attempt, so you siblings have to do the research... maybe a different GP, make the appointment, maybe a home visit? Try getting all three of you together to discuss things with him, so its not just you tackling it on your own and being ignored or shouted at (great way to change the subject). I don't know what's available in your area but maybe Age Concern/social services will.
Can you get some grief counciling yourself and some advice on how to deal with this situation?
Finally, because its worth repeating, Christmas, the season of massive guilt tripping is over. Its been hell because you all missed your Mum but you got through it. It was never going to be perfect so Let it go. these things take time, but Christmas added extra stress.
You don't have to worry about that for another year.
You and your DH can get back to your normal routines, and breath a sigh of relief that you don't have your Dad staying for 5 days, and all the arguments.
Wishing you all the best. Don't forget to take care of yourself during this period. There are lots of adjustments, but take it step by step and try not to worry about what is too far ahead.