You're not wrong to feel this way, but it sounds like that's how these people are. I doubt they will change - you've participated, stayed away, talked to them, and nothing works. In fact, your MIL told you to your face that you aren't part of the family, and the lack of baby gifts rubbed it in. I think it's time to get the message. They are not capable of extending themselves and loving people. Your husband knows who and how they are, and sees no point in fighting. I know you had very high expectations, but just because there is a large family doesn't mean there is a lot of love. It's really a power game with them - who's in, and who's out. That's why you and your children were ignored, and that's why you got this invitation. Notice that it's for a "virtual" shower, which means a way to get gifts without having to actually extend themselves or entertain anyone. A virtual shower can be fine for someone who lives far away when visiting isn't practical, but that doesn't seem to be the case here.
So, you can't control them, and all you can control is your own reaction. Stop fighting it, and surround yourself and your children with people who DO love them, whether in your family or with close friends who are like family. That's what we've done in our family. My brother's family is like the people you describe. They do send gifts, but what they do is spend a whole ton of money 2 weeks before Christmas, buy 5 or 6 of several different items, and then make piles to send to each family. Everyone gets the same books, calendars, whatever. We go to my mother's house, and see that she got the same things we did. My brother's wife's sister, niece, nephew get the same things too. She has even been at my brother's house when they do this mad gift-wrapping, gift-assigning task. It's ridiculous. There's no thought about what someone might like or care about.
I kind of grew up with this - my father's mother made it clear that her sons were priority, and her daughters-in-law were not. She even said to my mother, "I love you like you're my own, dear, but remember, you're NOT."
You can send a shower gift, or not send a shower gift. Either way, it won't change how they feel. If you send one, they'll gloat that you got suckered into it, and if you don't, they'll complain that you are mean or cheap. Either way, you lose.
It's sad, but you have to bury those hopes and expectations, mourn them, and move on. Wishing won't make it so. Meantime, you are making yourself miserable, and your girls will pick up that there is something wrong with your side of the family if they grow up seeing that something is lacking. They need to not feel rejected. If they ask, you can say that's how Dad's family is, but we are different - otherwise, celebrate what you DO have and build an extended family of your own.
Good luck!