I obviously don't know this person, but if it is a fairly normal person, it seems like you might be over reacting a bit. Is it possible you were invited and the invitation was lost?
Maybe it is regional, but I don't think it is rude to tell somebody if/where you are registered. Telling somebody about a registry is not demanding a gift, it is like saying "hey, if you are thinking about a gift, here are suggestions." I personally like to get that sort of information so I know what somebody wants rather than feeling like I have to guess and hope they don't already have six of what I chose. If she had written exactly what you were to send, or told you the amount she expects you to spend on the registry- that would be a different story.
It also doesn't seem odd to me to mention when you are due. I work with my immediate family and last time I was pregnant I got asked "when are you due again?" almost daily from the moment I was showing up until the day he was born. Most people don't remember somebody else's due date and maybe she is just aware of the fact that other people's lives don't revolve around tracking what is going on with her.
I would at least send a congratulating card. The shower is about giving to that child, not the mother. Even if you think my perspective is stupid and are upset with the mom, that really isn't the baby's fault and I don't think you mean to give the message that the baby is unwelcome. My daughter's room is full of personalized books and tokens that are useless to me but remind her that people loved her from the start. She is now 7 and she really appreciates it. I still have books from the shower when my mom was expecting me. Plus, if she rubbed a lot of people the wrong way- you might be the only one to send anything to that baby...