When his cousin got married my eldest was not on invitation just you get who was a baby. He immediately rang his siblings to see if only babies were invited but when other nephews and nieces were he was on phone and cousin sent her an invitation.
I have not posted about this.
Photographs were taken of all the kids but then specific sets and DH’s nieces took youngest out of my eldest arms and they all asked her to step out. I did not know this until two days afterwards when she told me how it made her feel.
So at this point the now 5 year old was a baby, meaning the Stepchild was only 4 or 5. That's very young to be holding a baby, and potentially awkward looking in photos. Photographs have been taken of ALL the kids by this point and the older nieces asked for a photo of them holding their baby cousin. Especially as the now 5 year old was a lockdown baby, presumably this 2020 or 2021 wedding was one of few opportunities for photos with the new addition to the family.
I've got similar pictures at family events where I'm just holding one baby and the baby's whole sibset aren't in every shot. I have pictures of me as a baby without my other siblings at weddings etc being held by cousins, aunties etc. It's just a normal thing that happens at family events. Not every child is in every single picture. That's just life.
And it could have been easily explained to a then 4 or 5 year old without it being made into such a big thing about her sister being "taken out of her arms" and her being "forced to step out" etc that OP is still stewing over years later.
My Mum, our shared Grandparent and half-sibling have pictures together just the three of them on my half-sibling's wedding day. My Dad and I were asked to step aside for the photo, by my half-sibling. I was a child at the time as half-sibling was an adult when I was born. It's not traumatised me for life and, as young as I was, I understood why it was a nice picture for them to have.
Likewise, I understood why my Dad and I weren't at the top-table, even though half-sibling never knew their father and my Dad was very good to them and looked after them from childhood so was the closest thing they had to a father. It was because they didn't want the awkwardness of me being on the top table and perhaps needing more attention from our Mum on a day that they needed her more. We were a blended family and this sort of thing is all just par for the course. Sometimes we did things together, sometimes separately. There was no insistence that everything be equal 100% of the time and that both of us had to be in pictures in all three sets of grandparents houses for example (given our age gap, my half-sibling never actually met my paternal grandparents and I never met theirs, obviously). Luckily, my parents explained things clearly from a young age so I didn't take everything personally. It's really important for parents to manage not just their own expectations but their kids too.
I was fine hearing..."Tom is Ashley's cousin but not yours, so they get Ashley a Christmas present. But Ashley doesn't get one from Sara, because Sara is your cousin, not Ashley's" for example. It's easy enough to explain that "your sister and you have different grandparents" to an almost 10 year old. She doesn't call her stepfather Dad so she already must know on some level that these are not her grandparents.
And there is nothing wrong with the other children in the family referring to themselves as half-siblings. That's how they see themselves and it's not up to the OP to police and express her unhappiness at how other people refer to their own family relationships.
It would be much better for her to focus her energies on building a connection with her oldest child's father's side of the family, particularly her paternal grandmother who was previously involved.