1) He's jealous. It's very possible, as this is your dog, not his. Right now your dog (and inadvertently you) may be getting a lot more attention than he is. Shake the mongrel dog that is getting the attention is possibly his way of getting attention, be it good or bad.
2) He honestly just hates the bloody dog. Not all ppl like all breeds of dogs.
As much as it may gall you to try this, I would use your brother's own vanity against him. I would tell him about something you can't seem to manage with your dog, but can he help you as he may be much better at it. You could be amazed at the change in his attitude.
Unfortunately, it sounds like your brother and yourself don't get along at the best of times, and it sounds like your mum doesn't have much experience with dogs, which is possibly making the situation worse?