I have a somewhat different situation in my own case - my BIL is an utter arsehole and has said some unbelievably vile stuff to me.
However, he's an arsehole to everyone, including DH and the rest of the family. MIL has, IMO, pandered to him for years to try to stop his outrageous behaviour - of course it hasn't worked, so now we have a mid-40s toddler-like man who throws tantrums and everyone just bows under it. However, if MIL stands up to him, then he escalates to the point of madness - standing in the street shouting and swearing at all and sundry, screaming at his mother, breaking furniture etc. He's had restraining orders out against him, he's been in jail, he's under good behaviour bonds, he's court-ordered to no longer drink alcohol - but all of that means nothing to him when his will is crossed and off he goes. So far he hasn't been physically violent to his mother but the verbal abuse is horrendous.
DH won't cut him off. MIL won't cut him off. I have done my best to have nothing to do with him and that will be for all time - he is irredeemable. But I can't cut DH and MIL off for still dealing with him - DH is trying to support his mother, she is the "weak" one - but is she? She's a victim of his abuse, as is DH, as have I been.
Bullies are hard to stand up to, especially when they're your own family. I can't entirely blame OP's DH for not managing it. It's at least something that he acknowledges to the OP that their behaviour is shit, rather than gaslighting her that everything is "normal" and she is just "hypersensitive".
Yes, he should have told them to behave themselves in a civilised manner from the outset - but none of us are perfect in our behaviours and interactions with others. I don't think the OP should dump her DH over this - but I do think she can make a unilateral decision at this stage to dump his family.