My husband and I also had a small wedding, afterwards we changed children's birth certificates to be "children of the marriage" (he is their father). For us, our marriage was the final tie binding all of us together as a married family. My children being part of that was a priority for me. So I understand that the children here might feel the same way.
As things are, this is not possible so personally I would focus on fair and make it equal for all the children. My family, we created. I would feel the same for joining two families together. So would have special celebration later that's fair.
Ultimately, it's always "my wedding, my choice" but at least this is a situation where people just want to share the joy with you OP