Typically, showers here are done before baby comes unless baby has arrived early so that baby is never there.
I've brought Corinne to one at 2 months old because I was asked to bring the kids. I knew E would be bored so I didn't bring her. Usually, I don't want to bring them. It's no fun and I can't socialize like I want to as they aren't old enough to sit through one without getting bored.
I also don't typically bring them to weddings as I like to kick back and not be "mom' for the night.
I would never bring my kids to a shower without them being explicitly invited, except for a very small baby...even in that case i would probably ask first. I don't remember any baby showers with children there.
I guess it depends on the traditions in the area. I would find it very odd to have to say on an invitation "no children please"...because IMO no one should be assuming they can bring their children.
I have brought non-mobile babies for nursing purposes but older kids are more of a hassle for me.
I would reply and say that you would love to show up but when you would show up will depend on your nursing. If I didn't have kids, the nursing aspect would not have occurred to me. I would just be thinking that I don't want a hoard of kids running through my house.
I know nothing about baby shower protocol but I would think a nursing infant is a different thing from a kid who can run around. I would check.
I scheduled my activities around nursing. Getting haircuts, dentists, groceries, lunch with a friend, going to the gym, going to a movie, dinner date with DH
... This was whether or not the baby was with me. I'd rather start off with a well fed baby. I have no problem NIP and appreciate the freedom when travelling or out for the day but I enjoyed it more at home in a comfy chair.
I started off all three babies very well fed, nursed them all, and I totally agree with Laurie. I enjoy doing many activities other than just lunching and haircutting and dinner dates, and some of those activities are not baby friendly. Babies are simply not accessories on can trot around the golf course, no matter how NIP friendly a mother is (and I am ~ could and did nurse anywhere). Babies are also not accessories who get a free pass places where their presence has been specifically denied simply because they are nursing. At 9 months my babies were walking ~ and nursing ~ But yes, they would have been QUITE a distraction from a baby shower focused on the mother to be. That is why we practiced leaving them early/using bottles of pumped breast milk/etc.....because freedom and the ability to attend events/have me time was and remains important to me. I would (personally!!!) Feel terribly trapped if my husband was unable to care for our 9 month old child for more than an hour~ there are many things I do in my life that required me to be away from my nurslings for an hour. If other people don't WANT to be away from baby, ever, that is a fine and valid parenting decision, but you can't then complain when you are restricted from certain events where children are not welcome, as hosts have the same right to make the decision to not include children as you have made to not leave your child's side.
And despite my lack of experience with baby showers, I can envision a scenario in which someone might not want ANY kids around. Maybe they want to hoot and holler and be loud, maybe it's an attention thing, who knows? Or maybe they just didn't think about nursing babies and it will be fine. I think it's worth a conversation to find out.