It doesn’t matter whether anyone else thinks you or your db or his wife to be are reasonable or not.
It's abundantly clear that they will consider your white with florals dress, similar to the one they saw at your mum’s house, to be inappropriate.
Maybe that’s a bit precious of them & maybe it isn’t, but that’s how they feel, so if you rock up in the dress you have in mind, you’ll piss them off.
I can imagine being irritated if I was on a limited budget, the dress was the only posh frock I had access to & there was no way to return it? In which case you have my sympathy.
Otherwise, I’d just be rolling my eyes a bit, wearing something else & saving the white with floral thing for another occasion. Problem solved.
It’s obvious that you dislike your new DSIL to be, which is your prerogative, but probably another reason not to create completely unnecessary tension at their wedding.
I don’t much like my SIL; not really her fault, she just irritates me & I dislike her politics. The feeling is mutual.
I would much rather avoid petty shit like this - it means we can chat politely at family events, which is nice for my brother & my parents. Absolutely no reason not to just shrug & wear something else.