I honestly don't think you're being too sensitive in this situation (and I have to stipulate to be fair, as I don't know about other situations) but what you discribed would be very annoying to me, even WITHOUT my thinking he was pushing me around. There are people who like to present as busy busy people, too busy to call but not to busy to blow up a cell phone in text, or email bomb for days. I think they're either confused about how long texting/emailing actually takes, are arrogant or possibly both. At any rate, it IS quite annoying.

That said....I'm curious where in the family unit your brother falls...is he the youngest? Older than you? It hardly matters but I would be interested in knowing if this is the first time he's shown such passive / aggressive tendencies because, that's what he's doing. It may not be to directly control you or even push you around in particular (unless he's done this many times before over other issues, then yes, I'd say it sounds like it's his way of getting his way/bullying you).

However, it could be (if this is NOT his pattern) that he is having difficulty dealing with the situation with your mom being ill, and is, in a small way trying to distance himself from it. Of course, that could be a pattern he's used in the past with other difficult situations. Only you'd know for sure.

At any rate, try not to let it get to you. He may want it to, so don't give him the satisfaction. He may not mean it to, so don't over-react to his issues. Remember, that this is about your mom, no matter how much it seems he's trying to make it about him. Hopefully, your mom will be better soon, and then if necessary you can deal with your brother, and maybe find out what it is that's causing him such stress, and fear, because make no mistake, the use of passive/aggressive is a learned response...and usually it's a response to either stress or fear.

Take care