OP, I am so sorry for your loss.
I do not agree that it is OK for him to have introduced a new woman into the children's lives so early on. That is not OK.
There is no acceptable time limit to meet someone else, but it is not acceptable to introduce them to children who are so early in the grief process.
My children lost their father at similar ages and they were very close to their step mum. She met someone 4 months after my children's father's death and introduced him to my children (without me knowing beforehand) and it was a messy situation. She had no responsibility to my children I know, but it did complicate their grief and caused a lot of pain for them.
Unlike my children's SM, your brother in law is responsible for the children's welfare and is showing poor judgment about their needs. It's OK to be angry and worried about that.
All you can do is be there for the children like I know you will be. No one can replace your sister and her children will never forget her.
They are lucky to have a lovely auntie like you, and once again I am so sorry for your loss, and the pain his meeting someone else so early on has understandably caused you.