I’m assuming that ex is the baby’s father.
You are not required to let her into your home. You are not required to introduce her to your baby. In fact you have sound reasons not to.
However, when your ex has access, you cannot prevent him from introducing the baby to her or letting her babysit or anything along those lines.
I can absolutely understand your reaction. But please also think long term.
Are you planning on remaining in the same area and will ex have regular time with the baby/child? If so, would it make your life easier in the long run to have ex’s sister meet the baby now? What difficulties would it cause with ex and mil and sister if you prevent sister from meeting the baby? Are they worth it? (Your answer may be yes).
Would it be possible/enough for your ex to negotiate with his sister - she must apologise first? (Your answer may be no).
Lastly, were the threats verbal or via text/email and did you report any of them to the police? Having done that may make ex’s family take sister’s behavior more seriously rather than supporting her. If you didn’t report them, do you have details of them written any where, did you keep a record that you could use? And is it the overt sort of stuff that could have warranted police involvement or was it more subtle?
That’s a lot more questions that answers, I am afraid, but I think you should consider all of those before making a decision. And please, thin’ long term and strategically, not just a short term emotional response. Although, the two might turn out to be the same.