I've been in your shoes. My FIL died in a car accident 7 months after DH and I got married. I was also giving my DSis support as she was going through a divorce having got out of an abusive marriage.
We couldn't see my MIL often because we lived a long way from her, but she used to speak to my DH for an hour every evening, and it was draining. He was also the one handling everything for her, as my BIL and SIL had recently had a baby and they had 3 DC of 3 and under.
MIL also became obsessed with blaming the police for not prosecuting the other driver, because she couldn't accept that FIL had pulled out without checking his blind spot. I knew this because the case was being handled by the solicitor I worked for and I typed most of the letter.
My MIL also threatened several times to throw herself under a car. It was just as well we didn't live near her as I don't know whether our marriage would have survived. I felt like a right cow sometimes; I tried to be supportive but I was drained. We were also going through infertility at the time.
I remember a conversation we had not long after the accident. A wise friend who had been a widow for some years said in a letter to us that MIL had a long, lonely road ahead of her. DH said that it was our job to make sure she wasn't lonely. I pointed out that he couldn't stop that, as he was her DS and couldn't fill the gap that her DH had left in her life.
And, like you, I've always struggled to get on with my MIL, as we are so different. (She's almost fanatically pro Brexit for starters.) But she has come through her grief and she's a lovely Grandma to our 2 DDs. (We adopted eventually.)
Maybe that's how your DH feels? You do need to talk honestly to him about this, as this resentment will eat away at you if you don't. 
