@germinal
I am soooo sorry for your loss. That must have been so hard. I may be wrong, but it seems like he has moved on way too fast. New woman, same name, already letting her stay over a lot. Very odd. Won't be long before she moves in, and it seems HUGELY unfair on the children. Seems like your BIL has replaced your sister as quick as he could.
Some people just simply CANNOT live without being in a relationship. I know some women who have this 'any man is better than no man' attitude, and some men also, who can't function without having a woman in their life, and in their house.
I know a woman (now 53,) who was with a man from the age of 30, and they were like soulmates; did everything together, no kids, lots of cats, 2 dogs, a bit of travelling, camping trips, very happy-hippy types.
He died of cancer (just 5 months after being diagnosed,) in 2017, and she wept uncontrollably for 5 days straight, and sobbed at his graveside at the funeral, and posted a pic on facebook 2 weeks after is death, with her holding a 4 ft x 6 ft blown pic of him over her head, with her crying, and 'R.I.P. my angel' as the tagline on the post.
Six months later, she had another man. Pics of them loved up, and going on day trips together, camping, and cuddling by the campfire, and pics on facebook saying #loveisgrand and similar things. Every one of the 200+ pics of her deceased husband, (and pics of him and her) was GONE from facebook, except one, within 5-6 weeks of the new man coming on the scene.
As I said, 6 months her husband had been dead before she started seeing this new man. And she moved on with someone who was the same as him in every way. He seemed HUGELY like a replacement. Not sure what her new man thought, about him being a carbon copy of her husband of 20 years, but everyone thought it was a bit odd.
Yeah it's her business, (before anyone says,) but people are still allowed to have an opinion on it.