It really doesn't matter if people like you or not as long as they are civil. There are people that we just don't connect with and that is okay. My MIL also was competitive with my husband as she was probably feeling bad that her son needed me more than her - perfectly understandable. So I found ways to complement her so that she knew that I didn't despise her (even though my thoughts sometimes were opposite). I think it's easy to read into situations if you have a preconceived notion. Because she is not allowed to stay at your home, I'm sure she feels like you despise her. No wonder she hasn't come to see the baby. It's hard for people to come to a place where they are not welcome.
Do whatever you can to treat her with the dignity and respect that is due someone who raised your son. After a while, it will get easier. It will mean a lot to your husband. One time I needed to write my MIL a thank you note and I added several paragraphs about how well they raised my husband. I bragged about what a good father he was and that they must have been great role models for him growing up. (I know there were times when they weren't the best parents, but I have had my moments as well, so what.) Ever since that letter, my MIL has been so much warmer to me. I know she still doesn't like some things about me but that is understandable. I grew up in the city, she has only lived in the country. I am in a different generation from her and have different food tastes, but she and I enjoy each other a lot more than those early days. You can bring out a warmer side of a person just by the way you treat them. Haven't you ever asked a checker at the grocery store how their day is going and then see a totally different attitude?
My husband loves the fact that I don't whine and complain about his mom anymore. When I need to vent about something about her, I just call or email one of my friends. I think it really annoyed my husband to hear me go on and on about his mom. He knows what she's like and can't fix her, so it was a helpless feeling when he would have to listen to my rants.
Make sure your kids think you are looking forward to them coming. It's really all about them and their relationship with their grandparents. If you make it more warm and welcoming instead of just tolerant, they will come more often and your husband and kids will benefit. If your MIL says something that irks you, then just assume the best not the worst. You can decide how to take her remarks. E.g. If she says, "Have you changed the furniture around in the living room?" assume she is complimenting your style and not criticizing the fact that it was better before. You can decide to make all of her comments positive or just let them bounce of your back.
My kids never got to have my parents come visit them after they were in school. My parents just aren't the warm grandparent type, so see your in-laws as a blessing to your kids. I had to.