I've read all your updates @HannahRose23 .
First of all, please stop enabling your brother and buying presents for him to give to your parents etc. That just makes you a doormat and a martyr and you won't get thanks for it.
Secondly, you are not being unreasonable to be upset that your mother has changed the plans for one evening of a 3 night stay when you were looking forward to a girly weekend away, just the two of you. But I can see (even if I don't agree with your Mum) that her reasoning would be that she has been desperate to meet the gf ( that is not unreasonable of her) and you are both in London for 3 nights, so why not spend one night meeting your brother and the gf when you were going out for a meal anyway? Absolutely unacceptable that she said yes, without asking you if you minded and getting an agreement on which night you all met up. Also unacceptable that she didn't even consider inviting you until you said you were upset, which would have meant leaving you on your own for an evening.
Thirdly, however, while going forward from this in future, having less contact, not trying to please your Mum/Brother etc or whatever you decide to do to take back control and look after yourself first, not last, sounds like the way to go, I'm not sure that this particular incident is the Hill to die on:
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Do you have a good friend that you can replace your Mum with for that weekend? If you just cancel everything and you haven't anyone else to go with, you will be seen as 'cutting off your nose to spite your face' and not just by your Mum, but most people you tell the story to. This will spoil your stand on this occasion. Yes, I know it's not fair, but you won't get them to change their attitudes and they will blame you entirely for the fall out. Pick your timing later
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if you do cancel the weekend, you still need to buy the wedding dress. Online isn't the best way to go for all sorts of reasons
I think, if it were me, I would still go with the original weekend with your Mum, make the best of it and rearrange which night you go to your favourite restaurant. Accept that things haven't worked out the way you hoped, take the higher ground and don't let yourself be resentful with your Mum and Brother during the weekend. This is especially the case if you don't have someone else to go with
Once that is over, take all the action you need to, to stop letting the pair of them walk all over you, by whatever means
I hope the wedding goes well