I'm confused. If she's asking you to do things, how do you know she doesn't like you? Is it maybe you don't like her or resent her? I'm just wondering, because again, you say she's messaging you to do things. This is a horrible stereotype, but married couples even now still turn the social life over to the woman. Doesn't always often, but often does. I don't live in the same state with my brother but all my communications with him are usually started by his wife. Just is. I have a nephew who got married a few years ago and moved to the next state south of me. They don't communicate with me really, but on those few occasions when some family happened to gather here his wife was the one who communicated with me, and I've never met her but once. Again, it just is. Now, if it's really true his wife doesn't like you and you appear to share this dislike, then you're going to have to initiate conversation with your brother and set up things that are just you and him, but realize that those of us who get married often settle into a couples life and do things as a couple most of he time. Again, not something that's always true, but is sometimes true. My Dad had no friends of his own at all -- everything he did was always with the wife he had at the time. Again, just was.
What sort of things does she ask you to do that offends you?
Are you in India, by any chance? There are very different expectations of women who become in-laws, there.
I, also, wonder what type of things she texts you to do. Is it social things or is she texting you, asking you to run errands or to do other things "for" her?
Ok we need more context to understand what's going on here. She messages you to do...what? If she asks you to buy her something on your way over or asks for any kind of help and you answer with "ask my brother to do it" it actually can sound rude and she has right to be mad at you.
Again being offended is subjective, so if you get offended at her for asking you to do "things" for her,then it's on you. It doesn't mean that she is trying to offend you or make you feel like her errand boy/girl. I have to agree with the comment above, I think you disliked this girl from the start and now you're trying to nitpick on her behavior trying to pass the blame on to her.
Sounds like she wants to treat you like family and herself like family - what is missing here? what she's asking you to do. the fact that you didn't fill that in sounds like you're griping that you aren't able to ignore her entirely.. Which would be counter productive if your brother wants his wife to feel like part of the family. Are you out of line here? If so, maybe you can talk about it here and figure out how to make things better for everybody.