Estranged mother

I haven't seen or spoken to my mom for the past 3 weeks due to an argument, which was truly stupid. Since she hates it to be talked back to, she has dropped me so to speak. I briefly spoke to my brother and he said the least I can do is try to fix it, because according to her I said a lot of hateful things. This is not true and over exaggerated. I have apologized but I know she never will. In every argument she always tells me I need her more than she needs me. Ironically, her mother -my grandmother- has said and done the exact same things! And my mother has gone through the bad depression phases because of things that were said. So I just don't know how she can't look in the mirror and doing the exact same thing.

This situation has come at the worst time, because for the first time I am pregnant and I wished she would be there every step of the way. My next ultrasound app. Is less than 2 weeks and my MIL has asked to go with me, I wished that I shared the moment with my mother first, ontop of it now I feel guilty for it all but still angry!!!

I just don't know what to do, how I should mend things with my mother. Just to show up and apologize again? I'm scared of being rejected again.