Could you put both a current address and a future address? I've seen people put temporary and permanent addresses on resumes. (We hire many students who have 2 addresses.) You might want to explain in the cover letter that you have a secured a place to live in future city so that they know you are serious.
The double address thing is something I've seen, too, now that I think of it, again with students. I guess if you're planning to move in with your brother for certain, it makes more sense to me to use his address--if someone says, "You live at X, right?" you could say, "I'll be moving to that location on March 15; currently I'm at Y." So, no matter whether you get that particular job or not, you'll be moving to address X on March 15. That would be an easy enough thing to mention in the cover letter, just a line or two.
I think it would be shadier if you weren't
necessarily planning to move there unless you got a job--using your brother's address in New York, your cousin's in Florida, your aunt's in Michigan, etc.. I don't know if that's actually wrong
in some way but it feels off to me.
When I help interview college students to be part-time interns in our office, I always ask if they have their own apartment in town. My boss doesn't like the idea of them commuting in from other towns--I think it's a little negative of her, but she feels they'll be flakier and more likely to cancel their shift on a given day if they have to drive very far. Plus if it's winter she'll worry about them driving in bad weather. And if anyone applies who isn't currently a student at our university--even if they have firm plans to start soon--they're out of the running entirely. I find it a little irrational, but that's how she is--I guess I was hoping other people in more regulated industries didn't have biases like that.