In personal opinion anyone who doesn’t like the mother is toxic to the child in one way or another. Try talking to her and find out the reason for her being hot and cold towards you
I feel like I’ve seen this scenario several times on here so not sure if it’s you who keeps posting the same thing looking for people to agree with you but personally I feel it’s his sister, she has every right to have a relationship with the children despite her relationship with you. As long as she treats them well it wouldn’t be an issue for me
I wouldn't let my baby be around someone who doesn't like or respects me (or vice versa) without me present. Doesn't matter if it's husband's sister or other relative. When my child will be old enough to make own decisions will visit or meet. Till then, no.
I've been in this situation afew times. I keep my personal feelings aside and let my child engage with them as long as there's no negative impact coming off it. I will be polite but take a backseat in the interactions myself.