It often needs to be more than "a room for the two of them." A 25-year-old minor league with a wife and two young kids? They need a two-bedroom apartment, not a room.
But you're right, it should not be difficult. More bluntly, it is not difficult. But the honest way to accomplish it would be to pay these kids a living wage/salary.
Put it this way: MLB currently allows clubs to carry 180 players on the domestic reserve list. A salary equivalent to about $15/hour full-time would pay these kids $30k/year - enough to live on, although not particularly well. $30k x 180 = $5.4 million. That's not chump change - but it's roughly equivalent to what the Phillies paid out in contract buyouts (to McCutchen and Herrera) last November.
Paying a living wage would address the housing problems. It would, at the same time, address the off-season issues that young players have - trying to balance training/conditioning with the need to take off-season crappy jobs just to keep food on the table. It would also (gasp! the horror!) bring MLB into more-or-less compliance with the kind of labor treatment that is expected (and often legally required) in other industries.
A club with a $200 million major-league payroll (or one with a $50 million major-league payroll) can bloody well afford to pay its 180 "peons" a living wage. That they refuse to do so, notwithstanding their obvious ability, and moral obligation, to do that, should tell us pretty much everything we need to know about MLB's ownership. These are not decent human beings. Not one of them. They need to be compelled to behave, at least minimally, as if they were decent human beings. That will require federal intervention.