Most baby showers ive been to thete os no children allowed.
I don't think it's rude being it's your choice but like the above said, keep in mind alot of people sometimes won't go then due to not having babysitters or you also might have hurt feeling so keep that in mind!
I don't think it's rude at all. It's your party. I agree to make sure you let people know well enough ahead to make arrangements and try to word it in a nice way. I would just keep in mind some people who have kids may not be able to attend even with advanced notice and not get offended if they can't. You'll find having kids means sometimes you just can't work it out even if you want to go.
No that's not rude at all! I put that on almost every invitation for previous events so my family and friends already know
Not at all, you could word it differently like adults only, cause some people find offense to anything. I wanted a child free baby shower, but I'm really ok as long as mine aren't there and I don't have to redirect anyone else's children.
Also make sure invitations go out early enough that those with kids have enough time to make arrangements for them.
No. If you don't want children there then its OK but you could word it better like inviting all adults to my baby shower or something like that