I think that you have the right to do whatever you want. But..
I'm curious as to why you even want to have a "meet the baby" party with your mother's side of the family, when it sounds like you really aren't that close with them and they don't invite you to family events? And, if their opinion of gift giving events for second babies is similar to your mother's, they're likely to just see you as gift-grabby?
Because although you say you don't expect gifts, you kind of blew that with the "but diapers are always welcome, if anyone asks." I think that may be what set your mom off with the "2nd showers aren't done" comments.
Your comments about the limelight seem off to me, too.. you would really leave your mother's wedding reception if your baby wasn't getting as much attention as some others, even though you say you don't want the baby circulated around?
I too think you're giving your mom too much "head space," and I also think you're worrying about things that haven't even happened.
I find that I sometimes start thinking in cliches and stereotypes, esp. with extended family. And then the reality is actually quite pleasant.
Have the "meet the baby"; don't invite your mom's side. Invite friends, etc. Enjoy the day.
Take the baby to the wedding only if *you* would like to introduce the baby to your mom's family, and only if YOU want to deal with wrangling the baby.
Your mom is going to be really busy at the wedding--brides are. They're getting dressed, going through the ceremony, walking down the aisle, getting pictures taken. They're not *available* to swan around the room w/ the baby in hand. You'll have an hour or more when your mom isn't even there. So go a little early, be proactive about taking the baby over to meet people. Then later, when your mom is free, the baby will have already met people.
but otherwise--don't worry about this in advance.