There is a dynamic here that is being repeated throughout these families and in your own relationship between you and DP.
YOU have taken responsibility for your husband's relationship with his family. He, for his part, has allowed that to happen.
YOU are sending presents to your husband's family not him.
YOU are sending them out the online invitation thing, not him.
YOU are writing this for advice. While DP sits quietly to your side and dwells on his hurt feelings.
In some ways, if you are controlling all the 'relating' to his family, then he is prevented/excused from doing it himself.
Which suits him as he is avoidant in nature, and not keen on dealing with his emotions.
You don't mind managing his family because it's easier and does not bring up painful emotions like your own family!
But perhaps you are trying to resolve your own problem which is a DP who is as miserable as sin mooning about the place being depressed and sad about his past. But not doing anything about it himself.
You keep saying going to SIL's etc - but wait? Don't you mean going to 'DH Brother's house'? But you haven't mentioned his Brother, you place the 'power' with the SIL for some reason.
Again notice the Woman is blamed for the bad relationships not the Man. His brother chose a woman who would manage his relationships for him too.
The 'powerful' figures are his mother, his SIL and YOU - all women.
The Men in the family are all allowed to sit back and no-one gets angry with them. They take a passive role in relationships or huff or act out their hurt feelings until the woman gets activated to act on their behalf.
DP's Dad is the one he he should be taking umbrage with. He cheated on his wife.
Logically, your DP's mother had a 1yr old, then she had another baby - suddenly 2 under 2yrs of age!
I suspect DPs mother got angry with the children so that she could 'allow' her cheating husband to stay.
She wouldn't get angry with her husband so took it out on her baby son. Your DPs sister might have been able to take on the mother and give her as good as she got, but your DP may have been more sensitive of temperament.
She didn't stay because of your DP.
She stayed because her personality says that she values any relationship rather than abandonment, but will kick up hell inside that relationship and make people's lives a misery.
She may well have told people she stayed because she was pregnant.
Relatives tend to believe their own beliefs about something rather than seek feedback about the truth of the matter.
My advice. Move on with your lives - if you value having family around and enjoying those relationships for the most part, then find a way to keep contact.
Be aware that DPs family are different from yours. They are avoidant by nature. It may well not occur to them to answer emails, send thank you cards, gush over presents. It's not that they don't care, it's just not in their nature.
Your DP has issues, but he'd be as well to go and get therapy for himself and work through those. Then'll he feel better placed to take back control of his own relationships with his family. If he's depressed he should consider antidepressants.