I think she has a form of OCD with certain things as she's very rigid and won't budge
I don’t think you do anyone any favours by pathologising a 2 year old. At this stage she is learning about the world, what is and isn’t ok, what she likes and doesn’t like, how to talk to people, how to get her own way or not.
Toddlers are rigid, because they don’t know yet that there are lots of options most of which are ok, they tantrum because they feel overwhelmed and don’t understand feelings or how to express themselves fully in all situations - because they are learning all the time about every single thing. They aren’t expected to be emotionally intelligent, or to know what’s a big deal or not - because they are learning and need adults to guide them.
In this situation, if you knew your daughter was particular about where she sits you should have asked your brother to sit on the other side if you when he approached the table. That one thing would have avoided the whole situation and not left your 2 year old trying to figure it out.
Given you didn’t do that, I would have helped by daughter explain that she wanted to sit there and, if brother wouldn’t move, I’d have made space for her to sit beside me and helped her cope with that as best she could, including removing her from the BBQ if she
You seem to think it was an either/or - she gets that seat and all is well or she tantrums and everyone needs to deal with it. Tiny little people need to learn how to cope with great big feelings, adults avoiding those great big feelings, or labelling the child for having them is pandering and teaches the child her feelings aren’t safe - your brother was an arse, but there were a dozen other ways for you to deal with it that would all have been better for your daughter in the long run.
As the adult, and her parent, it’s your job to figure it out.