Disclosure: my first reaction is, this doesn't sound like a super compelling idea. This solves a problem for a bigger investment & higher risk than your current solution (staying with relatives/couch surfing). I *am* a fan of going the 2-family route if you purchase a house that you will live in immediately, that can help a lot with your own mortgage payments. Whatever you decide, do your homework so you are confident & satisfied with your decision - the emotional tug of hometown may be enough of a positive for you to make this decision about more than 'just' the money. With my biases in mind...a few more thoughts on the $ and logistics
#1 check with your hometown regulations. Where we live you have to register any rental, and the manager of record must live (or base their business) in the county. In some areas to be completely legal you need a certificate of apartment occupancy (initial inspection + annual reinspections by the city). In other areas, you can do almost whatever you want. A call or email to the local code enforcement department might be a good place to start.
#2 also, cash flow with a rental can be unpredictable, since maintenance & repair expenses can be "lumpy" (many large but hopefully infrequent expenses, some that are hard to predict eg plumbing failures). Agree with the long term return figures (I might use 5% for the market, but close enough!!) - in my experience, you create wealth in real estate either through sweat equity or by being able to pay cash for an un-financable (that is non-habitable) property and then fixing it or providing financing to a buyer who will fix it. Doesn't sound like either of these is your situation.
I'm guessing for most people this would not prove out financially, but it *could* be a good financial idea for you:
IF your hometown real estate market is currently depressed,
IF there are factors (new employers or industries, etc) that suggest it will become undepressed soon,
IF you are 90%-plus certain that you will eventually live in the house full time,
IF the likely near-term rental income will cover financing, taxes, any utilities paid by landlord, maintenance/lawn/snow and some payment to your brother for his efforts (don't forget a vacancy allowance and closing costs when doing these calculations), and
IF your brother is handy, good with toilets, and either a people person or a good enforcer.
Even if the answer to all these is "yes" it might not be super-compelling if you are looking to have a 'no worries' situation. If the answer to all is "yes" and you are willing to deal with the increased hassle, proceed.
The rental income math can vary a lot from place to place - where we live now, annual rent roll/acquisition cost runs about 40-50%, where we used to live it's more like 12-25% (gross rent before any expenses but after a small vacancy allowance). After expenses the numbers get a lot smaller (and sometimes negative, that's what you want to avoid)!
#3 this is DIFFICULT. managing a rental even from nearby can be a hassle. It is not impossible though...much will depend on your brother or local manager
#4 Different areas have very different approaches to legal vs. not legal 2 unit buildings. In some areas a non-official unit is fine, in others you will have many troubles and there is a big difference (which should be reflected in selling prices, but not always in asking prices - invariably the sellers don't think it should be an issue). If you *do* decide to go ahead, find some folks who own multi-family units in your area and ask them how it works (or a friendly RE attorney may be a good source - depends on the attorney though).
Finally, the lender will almost certainly view this as an investment property since it will not actually be owner-occupied. Legally it may indeed be your 'primary residence', but 8 weeks a year by you plus a separate occupied rental unit doesn't meet most lenders' definitions of owner occupied. You may want to create a corporate entity (LLC or regular incorporation - which is easier depends on State law) to do the transaction and operate the property, that way you can treat the operation as a business which is likely beneficial from a tax standpoint. Check with a tax professional for actual details!!
Overall, even if living in your hometown is your eventual goal, it seems like waiting until you are actually moving in full-time has little downside risk compared to the idea of buying something now.