For a number of years I was very involved with an on-line forum, which folded a couple of years ago. Some of the people there I did meet up with in real life - others I am in contact with on FB.
One of the men on the forum often talks fondly of his wife - and was devastated when after a short period of illness she was diagnosed with terminal cancer. Sadly, she didn't have long - a matter of weeks from diagnosis till her death. Their children were in their mid-late teens, and when their mother was ill and dying the father spoke of them as being young children and how hard it was for them to lose their mother at such a vulnerable age and so on. All as you would expect and it was a traumatic time for the whole family - quite understandably.
But - within about 3 weeks I think it was, of his wife's death - he was actively looking for a new relationship. The way he talked about his children turned around - now they were young adults, as good as independent. 6 weeks after his wife's death, he proposed to the girlfriend and she accepted. All photos of his wife and other personal items had been removed from the house by this time - in case the girlfriend was upset.
This man could not understand why his teenage daughter was distraught, and that his teenage son had withdrawn and wasn't speaking to him. He had no thought at all for them, and their grief for their mother. I just knew him from this on-line group, and up until this happened he had always seemed a pleasant and sensible man who loved and cared for his wife and children.
I was one of two women on the group who did try to persuade him at least to slow down the relationship and not make so many radical changes to the family home. He and the new woman were planning a total redecoration of the house. At this point his daughter left and went to stay with her aunt. The son pretty much stayed in his room when he was at home and spent most of his time with friends.
At the time, I did look into this phenomenon, and indeed it is a thing. Men, often whose marriages were happy ones, remarry or settle down with a new woman within weeks or months of their wife's death. They are happy, but their adult children are devastated and feel that their mothers have been negated or made less of. It's the speed of moving on and the desire to remove all traces of the deceased wife which families find so disturbing and hard to deal with. And all of this when children, of whatever age, are usually still very much grieving for their mother.
On thing that did strike me in this man's case, and again reading about this today, is this. I would have serious doubts about a woman who would get into a relationship with a man, knowing that his wife had died only weeks earlier. No matter how lovely a guy was, how much I was attracted to him - if he was recently widowed, I would back right off.
Sorry, a bit of a ramble post, but I remember how weird and upsetting it was to see that other man go from bereavement to "hey, I'm engaged!" in a matter of weeks, and be completely oblivious to the effect on his family.
I'm sorry, OP, both for the loss of your mother, and for this situation which must be really difficult for you and your sister.