Don't do it. Just (to twist the well-know phrase) don't do it.
You're correct to worry about her brother. And it's not just that he might not have good credit. There might be other issues that would lead to your turning his application down: drug use, sex offender, etc. That's too much of an unknown.
What could you do to reduce the risk? Not much. You could keep your lease the way it is, which probably says that all adults must receive approval. You could hold out for that, but what happens when, a month from now, the brother applies, you review the application, and you turn him down? She'll be angry, and might decide to break her lease. He'll be angry, and might move in anyway . . . in which case you'd have to evict him.
Besides, and I'm just guessing here: In what sort of situation might a man (with a family) need to/want to move . . . not now, but in a month? I'm guessing he's facing eviction or foreclosure. He may also be unemployed. Yes, I know lots of decent people have been foreclosed upon. But I'd, at a minimum, want to make sure that I knew everything about him. And, at this point, you don't. Now, you could always ask him (and his wife, if he has one) to complete an application now. That'd be OK; he applies now and just moves in a month from now. (Assuming his credit check and background check are OK, and so long as references from previous landlords--if that's the case--check out) Is there any reason he doesn't want to do that?
Finally, is your house big enough for all of them? At 1,600+ feet, I'm guessing it may be a 4-bedroom home. You'll have the woman who's applying. You'll have the brother and his wife. You'll have their children. You might end up with a very crowded home. Certainly, you'd have more than your fair share of wear and tear.
So, bottom line, I wouldn't do it. If you're really tempted to, then have the brother and any other adults submit an application and check it out closely before agreeing to anything. And even then, I'd probably increase the security deposit or require another month's rent . . . depending on what your local regulations allow.
Hope that helps.