Private or Semi-Private room in Nursing Home or Assisted Living...Difference?

First....after hours of Googling, I was fortunate enough to find this site...the information has been of incredible value and I will be armed when I go against the VA to fight for my 92 year old mother's rights. Thank you.

My mother is 92, has an income via teacher's retirement and social security of $23,000 per year....my deceased father served 4 years in the Marines during WWII. Net worth (cash and stocks) is less than $5,000. She fell 4 months ago and suffered a very bad concussion, no broken bones thank God. But, as a result...and because of an arthritic knee....she can no longer safely walk, and is in a wheel chair. Her knee "buckles" with no warning and she falls. Her orthopedic doctor has advised her, and has told my wife and I..."don't let her use a walker, or a cane...she will fall....stick to the wheel-chair."

She can no longer live by herself, and (after being released from 8 days in the hospital) is at a nursing home in her small town in East Texas. She will remain there, or go to an assisted living center in Tyler, TX, or in Houston. This will be her choice.

I took all of the necessary steps to put her in Medicaid, but did not file the forms because I learned from an Assisted Living manager about "Aid and Attendance," Wow..what a far better solution.

Sorry, this has taken so long to get to the question....If we had gone the Medicaid route, she would HAVE TO BE in a semi-private room at the nursing home and could NOT be in a private room even if I paid the difference. Does the VA make such a distinction? Could she be in a private room? Or, if she moves to an ALF, could she get a larger private studio, or even a 1-bedroom?