That's really interesting - different regions, different traditions/ideas.
Here, alcohol and kiddie parties don't mix. I don't think most parents in our area would feel comfortable dropping off kids at birthday parties where alcohol was going to be served. I wouldn't think the host would be comfortable being responsible for a bunch of kids while alcohol was being served to the adult guests, either. One unattended drink that Aunt Christine accidentally left on the coffee table and little Johnny thinks it's his fruit punch would be a nightmare, especially if the parents are not at the birthday party. But, again, where something is commonplace in one area, isn't in another and vice versa. If everyone is comfortable with it, then there's no problem.
At baby showers, I can see it being more commonplace than kids birthday parties to have lighter alcohol being served - because it's mainly all ladies who are legally allowed to consume alcohol (not kids). But, again, here it isn't common and most baby showers take place in the late morning or early afternoon.
If it isn't a party where the main focus is the children and the party is later in the day (late afternoon/night), it is typical for alcohol to be served.