Long-term rehab. What do we do?

My husband had both hips replaced and was up and walking the next day. He had no inpatient rehab. He had in home physical therapy a couple of times a week for two months. he was about 65 when he had it done.

I'm not clear as to why you would think that your mom would need longer than 7-14 days to be able to return to her home after having just a partial hip replacement.
I had a full hip replacement at the age of 58, and they had me up the same day walking and had me go home the very next day, where I had my daughter stay with me for about 10 days. I also had to go to outpatient PT a couple times a week for a couple months. I too was still caring for my husband at that time(at home)who was in the throes of his decline from vascular dementia, and about a week after my daughter left, my husband ended up in the hospital for a week, and because his speech was so limited, I felt I needed to be with him to be his voice, despite the fact that I couldn't drive yet(due to my surgery, so depended on my friends to take and pick me up)and had to walk extremely slow using my walker to get to his room and back.
It was a crazy time, and looking back on it, it's amazing what we humans can do when push comes to shove, so I wouldn't worry too much about your mom. She's very young and will do just fine. I think you may be over thinking things and underestimating the strength and determination of your mom. Us humans(and women in particular)are quite resilient.
Wishing your mom a quick recovery and the very best.

The facility may be operating under some kind of formula, e.g., hemi hip replacement = 7-14 days. I don't believe that's a Medicare requirement. I think you could appeal to go up to 21 days based on your mother's circumstances. Medicare will cover home health for a period after that, including PT, OT, and a nurse if needed to monitor recovery. Your mom might have to hire someone for a few days or weeks to help her out at home if she feels she's not ready to be entirely on her own, not necessarily a licensed medical person but a home health aide or homemaker service. But at her age, unless she has some other complicating medical conditions, 7-14 days with in-home PT after that should be enough to get her well on the road to recovery. My husband had the same surgery several years ago, when he was 80, and he also has Parkinsons. He had a Medicare Advantage plan and we had to fight to just get him covered to go to rehab.--they wanted him to go straight home! We actually had him go to the rehab place while we were appealing, and the documentation from the rehab facility was what ultimately swing the decision in his favor. Be sure your mom gets a home evaluation from PT and OT (Medicare will cover) to see what temporary modifications might be needed. For example, with hip precautions after this kind of surgery you are not supposed to sit with your legs at an angle above 90 degrees, so some toilets are too low so she would need a toilet riser seat. She might be safer/more comfortable using a shower chair rather than having to step over the side of the tub (if she has that kind of tub/shower combo). Etc.

My dad had his hip replaced when he was about that age way back in the 80's, if I recall correctly they had him up and walking the very next day.

Why do you think that a week or two in rehab won't be enough to get mom walking again? 65 is pretty young. Does she have other health issues?

Ask the hospital if they are sending her to ACUTE rehab, which may be why the short time frame. She would then be transferred to sub-acute for longer term therapy.

Once your Mom has entered rehab contact the Social Worker who will help to inform you how many days medicare covers. Normally this is up to 21 days in the past, so I can't be certain why you were informed of this ruling. Medicare puts out to every citizen on its roles yearly a handbook explaining rules and coverage. Call 1-800-Medicare to ask for a copy. You can also ask a lot of questions about coverage online.
After Mom is in for about a week there will be care conferences with all at the rehab. The MPOA for Mom can be included. This will help explain meals, meds, PT, OT and how measurements of need and progress are made.
It should be made clear to Social Workers that Mom needs to be self caring on discharge and lives alone.
You may need for Mom to get some home help and home visits from medicare for PT/OT in home. Some of this will be self care cost. Expect to pay upward of 30.00 hour if using an agency and most have minimums, say four hours three times a week for simple cleaning, walks, simple meal prep; ask agency at that time.
Try to take this a day at a time while still staying ahead of it (I know, makes no sense) but know much depends on her progress, some in home hired help may be needed on discharge, discharge planning will help explain the rules and work with Mom's unique situation. If Mom does spectacularly well they will want earlier discharge, but if she does very poorly they may "give up" so steady as it goes and contact Social Worker on day one to stay in contact on Mom's case.
Good luck.