We've been discussing this somewhat here, and the thread might give you some additional options to consider, such as low income senior housing, etc.
http://forum.mrmoneymustache.com/ask-a-mustachian/financially-supporting-aging-parents-during-fire/We wavered on this very decision, and finally did purchase a second home for my mother (65K). We had about 20K more take home income than you do at the time, but we had no down payment. We did, however, have our own home, 15 yr mortgage with about 40K of equity. We 1) refi'd Mortgage A to 30 yr to free up cash flow; 2) took out a 20K home equity loan against the A house's equity as a down payment on the B house; and 3) purchased the B house on a 30 year mortgage to keep payments low.
Of course, then we had a much bigger debt load. To deal with it, we 1) slashed spending; 2) paid off the home equity loan in 2 years (because it had around 6.5% interest rate); 3. After a couple more years, we refinanced A house again, back to 15 yr with a very low interest rate; and 4) simultaneously pulled ALL the equity available from house A again, and this time it was enough to completely pay off the higher interest mortgage on house B. So now we are back to one 15 year mortgage, at extremely low interest, on house A, but with less equity in that house. And we now own house B outright.
This was NOT the only option available. 1) A much cheaper option was to have my mother move into low income senior housing, with or without cash subsidies from us under the table. 2) A more expensive option would have been to have her just rent like a normal person, with us subsidizing a big portion of that rent and or utilities. 3) The cost/benefit of actually buying a house for her has just about hit the 'break even' point for us about 6 years in (we could get out of the house by selling it, just about the total of what we put in terms of mortgage/fees/taxes/upkeep costs, etc). 4) The final option we considered was selling our own house, and moving into a much larger house, specifically configured with a an in-law type suite, etc. Or buying a bigger house and remodeling. Something so we all shared the same living space. I suspect the 'break even' point on that would have been pretty similar.
I would not recommend buying any home, much less a second home, unless you are very financially stable and have solid income prospects. I would not recommend buying any home unless you are sure the occupant will be remaining in that location at least 5 years or more. I would not buy a second property unless you will be in close proximity and have the time and cash flow to be sure the property is properly maintained. I also would not buy a home for someone else unless I was completely confident they would be open and cooperative about their finances, and would not make stupid decisions when I wasn't looking. I would not recommend buying a second property to any but high income earners in most markets in the country (Texas real estate is very cheap, the state's senior care programs are limited, and that played into our decision).
In our case, it turned out to be good decision overall, though not necessarily the cheapest in terms of raw numbers, and we have reached the point where our sunk costs are zeroed out. HOWEVER, we are periodically facing the prospect of a move to a different state. In that case, we will deal with the exact same dilemma all over again in more expensive location. If this were to occur, we do NOT anticipate purchasing another alternate property, but would have to rely on one of the other options outlined above.