This actually is DirecTV's fault. They started up the whole "let's give everyone a billion HD channels" campaign. They never had to worry about the old, inefficient 6 MHz cable channels - DirecTV always required their digital box, and the DVD recorder your mother has never worked with DirecTV. They took advantage of their ability to offer only the more efficient service to gain significant market share. So much so that the cable companies had to respond by switching from the old, inefficient 6 MHz cable channels to something closer to what their very successful competitor was offering, i.e., new, efficient, 600 KHz standard definition cable channels and 3 MHz HD cable channels.
The math is unfortunate for your mother: People who want lots of HD channels contribute a lot more to profit than people who just want the basics. Our capitalist economy's strength rests on its vitality, and that means giving the customers what they want based on how much they're willing to pay for it.
There are alternatives, but they're not cheap. Your federal government requires cable television service providers to offer an inexpensive means of tuning in cable channels, separate from the DTA that your mother has. It's called CableCARD. It is possible that your HOA made an explicit agreement with Comcast to prevent you from getting CableCARD - if they did, then your mother should complain about her HOA to her neighbors, because that's a really stupid thing they did to their own residents. However, even if you can get a CableCARD, your mother's DVD recorder is surely not properly equipped for CableCARD. You'll need a reasonably modern recorder, and even then, the manufacturers charge a lot extra for that compatibility.
The best approach, I feel, is going with the cable company's DVR, assuming that option is available. While you can buy your own recorders, still, there is simply too much going on in the industry these days, as it modernizes from 1950s technology to 21st Century technology. Wait until the churn dies down a few years from now before investing in a new recorder.