I'll ask you the same question I always ask the prospective buyers on House Hunters (not that they can hear me), which is "what really NEEDS to be done and what do you merely WANT to do?"* In your case, it's possible the roof isn't in top condition and actually needs to be replaced or else there will be leaks and structural damage, but do the hardwood floors *need* to be redone or do you just want to replace them because of the aesthetics? My other thought comes from HGTV shows...it seems like whenever a contractor gives you an estimate, something else will be discovered that will add to it. So suddenly the house that's at the top of your budget might go way, way beyond your budget.
* honestly, I'm the wrong person to even be talking about this because the last time we made any changes to our house--in this case, a bathroom remodel that involved replacing pretty much everything and repainting--Mom was not just alive but WELL. So we're talking maybe...25 years? Dad and I are both VERY much "if it ain't broke, don't fix it" and tend to ignore things that just need a little, ah, beautifying.
Since it sounds like neither you nor your mom absolutely NEED a new living space right this minute, I'm inclined to agree with your brother: put in a really low bid on the house you think would be the best fit for your family, and if they don't accept, then you're no worse off than you were before.