How do you deal with your parent/parents having a relationship with them but you not wanting them around your own family?

Here's my story. I have a half sister( Moms daughter)  who I don't want to have a relationship with at all bc of the bad crap, and her coming in our lives only when she needs something or coming around every 5 yrs or so. She has recently reappeared to build a relationship with my incredibly vulnerable mother (my Dad just passed) saying she wants a family bc she has no one (she has 2 kids no SO) only my mom but I won't let her be a part of our family. She has other sisters who she has had a relationship with on and off but it's always wishy washy and it seems when she doesn't have a relationship with them is when she comes back to my mom. 

How do I keep the relationship with my mom without her getting upset that I don't want a relationship with my half sister at all, ever?? 

Thanks for the help