The answer to your question, regarding your mother’s possible need for supplemental oxygen at high altitude, depends in large measure on her current blood oxygen levels. There is a significant difference in available oxygen in the air at 7,000 feet compared to sea level and if her current blood oxygen pressure is 70mm or less, she may well need supplemental oxygen. If the pressure is 70 or less, she could still have a “normal” blood oxygen saturation at sea level , measured by an instrument called a pulse oximeter. Having said that, it could be helpful for her to have an oximeter measurement while walking.That she “gets winded while walking” suggests that this may be the case. If the saturation falls below 92 % at rest or with exertion at sea level, she will definitely have problems at an altitude of 7,000 feet, especially with even minimal exertion.
She will need to have arterial blood gas measurements. If that shows an oxygen pressure of 70 mm or less, there is no guarantee that her oxygen level at altitude would be safe. You should discuss this with her doctor.
An apt comparison is this. Most commercial airliners are pressured these days to the equivilant of 7,000 feet. If your mother has traveled some distance commercially recently and experienced no distress either at rest or walking to the rest room, that would be a good, but not definitive sign.
If it is determined that she will need oxygen at high altitude, and I believe that will be the case, she will also require oxygen during sleep, if you are at 7,-000 feet overnight..
Should she make the trip the best strategy is to spend as little time at high altitude as possible, yet still enjoy the experience. A couple hours should accomplish that. You should arrange things so that you spend the night before at 5,000 feet or less, go to the rim for a couple hours (with oxygen) and then that same day, return to 5,000 or less, less than 3,000 being ideal.
Good luck