@GreenWeaver - I do think that wedding gifts for a second marriage wedding is fine. I disagree with the notion that a second baby shower should not be held. I had a baby shower for my daughter that was given by a friend and I was also given a second baby shower when I was expecting my son from a coworker.
Both offered to give the shower and I did not solicit anyone to do this. They really wanted to do this and it was a lot of fun. I think that it depends on the circumstances. For example, I don’t think that a member of the family should give the shower. It is probably better for a family friend to give the shower instead.