Grandmother problems

Last year my (ex) boyfriend's mom and I got into it (the reason why is a long story), and she called me all these names like fat, bitch, selfish. I tried to bite my tongue because this is my boyfriend's mother - the one thing I did say was that nobody likes her, and she turned that around on me. But it's kinda true - she acts like a teenager. Anyway, from that point on I never really forgave her, always keeing my distance trust-wise. When I got pregnant, and now that I'm due any day, she acts like she wants to be my best friend and I'm just not comfortable with it. I see the way she is; two-faced and backstabbing. Just last week she was nice and friendly to my friend's face and then went and talked shit about her to my bf's cousin. I try to be nice and I grin and bear it when she touches my pregnant belly but I just don't want to spend more time with her than need be. But what I'm wondering is, should I get over it? Obviously she will be around my baby, which makes me nervous, because I don't want him growing up to be like her, or like anyone in their family. I don't know. I feel like I'm not making much sense.