How many kids do you think your guests will bring? If just a handful, then it's probably not much of a concern. Once you get more than that, you may want to let the restaurant know and plan for something to entertain them.
My shower is in a couple of weeks and I'm pretty sure there will be kids at my shower but this is typical for my family. I am allowing my son to come because I want him to feel like he is completely apart of my pregnancy. As for RSVP I think that is a dying concept, sad to say. If it's not for a wedding most people wont!
Me personally, I don't like when people bring their kids to showers of any kind, and I don't bring mine. TETO, but I don't feel that kids belong at just any and everything.
Have your host specify on your invitation that it is an adult-only event and to leave the LO's at home.
I don't feel that kids belong in a shower and I would assume only the person who's name is on the invite is invited. That being said, I hosted a baby shower for my cousin last month and two girls showed up with their kids without even asking if it was okay. It was just two of them so it wasn't a big deal for me in terms of food and space but it just showed me not everybody feels the same way I do, they will just do what they are going to do.
My shower is at my MILs house and she told me she prefers no kids. I have a few friends that want to or need to bring their kids. I wish they would leave them at home but whatever I guess they will be entertaining if nothing else.
Re: Kids at baby showers?
Have your host specify on your invitation that it is an adult-only event and to leave the LO's at home.