We just hired a live-in caregiver for mom, but mom is in the hospital and rehab is next. Do we pay and keep her with us, or let her go?

If your intention is to bring your mother home, allow the aide to start with daily visits to the facility. She can be of great help to you and your mom during rehab.And transitioning whether it is to home or another facility. Allow her to work the same number of hours you were originally contracting for. Let her do moms laundry. Ask her to keep notes on what goes on at the rehab. She will become a familiar and welcomed face if she is there through it all.
I did this with my DH aunt who is now in a NH but I didn’t want to lose her aides and I didn’t know at the onset what would happen. She actually still has one of her private aides who works for the hospice company we use. It has been a win-win for my family.
To me, your mom will be much better cared for if you add the aide now and you will have great support. I assume your mom has good insurance and mom won’t be out more money than she would have been if the hospitalization hadn’t happened.
Also, a good private aide can be difficult to find. She needs her income just as you or I would.
It is a unique opportunity to have an aide plugged in from day one and can set the stage for an ongoing good relationship.

I was in this situation a few years ago. I am an only child, so for me it was worth paying the caregiver to come sit with my dad in rehab, do his laundry, run any errands etc to keep her on, and then she seamlessly moved into caregiving him once he was back home. I did work out a reduced pay schedule for the 2 weeks he was in rehab. But it helped me and my dad both.

This is exactly what happened in our case. My father fell and had to go to the hospital and started rehab. Our caregiver is through an agency so it's costly but we didn't want to lose her. And we owe her a lot for how she's cared for my father. We decided to have her keep her regular hours and asked her to visit him in the hospital. It was quite a distance from dad's house so we gave her money for gas as it's so expensive. Unfortunately, his head injury was too serious for him to continue with rehab so he's home now on 24/7 care and she's on one of the shifts.

If your mother can afford it, you might consider having her stay with your mother through hospital and rehab. Most places are understaffed and she can keep her eye on any less than acceptable care. It made me feel less anxious about him being in a clearly understaffed facility.

with it beings so hard to find a good reliable person, I would continue to pay her. The hospital and rehab costs should be covered by insurance, and the caregiver can go to the hospital and be there with mom. Believe it or not, having someone keeping an eye out in the hospital and rehab is important. Patients get better care if the staff knows that someone is watching. I am speaking from real experience as both a professional who worked in the field, and a former patient.
I am 88 and fell and broke my hip. It was replaced during Covid. The month in rehab was so bad that I wrote a review in Yelp of the nursing care. The post was read by the marketing people, and several were terminated. If I had been able to have my caregiver, I would not have received such treatment that I had no way to stop until I remembered Yelp on the internet. Mom will appreciate the extra attention to her care.

Having her spend time with your mom in rehab not only gives your mom private help and eyes it will give them time to bond prior to going home which could be a real advantage. It may help the transition home and home exercises and PT go more seamlessly and continue too. While it does seem like an unnecessary expense I can tell you it’s a luxury I would splurge on if we could swing it!

It will be worth it to keep her, so for the time being I would mostly let her consider it a paid vacation ( think of all the jobs out there where employees are offered this- caregivers who are caring for our loved ones should definitely be afforded the same appreciation) perhaps have her visit there several times and be plugged back into action when it’s getting close to the time your mom will be getting out so she can be in the loop of info for as smooth a transition back as possible.

I have been in a very similar situation but without help lined up. Do whatever it takes to keep the help! As they say, good help is hard to find. Actually it is near impossible.
although your loved one is in rehab, she will need support there. Even great rehab locations are short on help. You need constant eyes on your mom to ensure she gets proper care. If no one shows up to check you can’t assume care is doing everything needed. When my dad was in rehab someone went every day. Once he got meds meant for someone else. Or another patient kept going in his room looking for his wife. Things happen and you will need help.
I agree that keeping the help on is a luxury but it will help you sleep better at night.
best wishes

If you continue to pay her, get her to go sit at the rehab with mom. Always best to have observation of mom's care in any kind of facility. Pay attention to the meds mom gets, if her personality changes that might indicate urinary infection, etc

Hard to find good help, so if there's a way to keep her - do it. You might even offer her a lower flat rate per week that lets her off the hook for working, but ensures she comes back when mom released....and get a contract signed to whatever is agreed to.

My family was in a similar situation 16 years ago. We had a wonderful live-in caregiver for a few months when my 89-year-old mother was diagnosed with West Nile fever. Mother was hospitalized and in a nursing home from the end of September to the middle of January. My sister and I chose to pay her until our mother returned home. She stayed in mother's house for those months. She went to the hospital and or rehab center to be with my mother on a daily basis. Mother recovered and lived for another 1-1/2 years. We were never sorry that we did this. My sister and I are still in touch with this wonderful caregiver. She is now retired but still part of our family.

It took YEARS????
Are you able to afford it?
If the answer to both these questions is yes, then I would HAPPILY pay to keep her. I would tell her to consider herself on paid vacation while Mom is in rehab. If Mom comes out of rehab in the meantime your well rested and very happy and willing caregiver will be waiting.
Not everyone can afford to do this. If you CAN, I think it a wonderful expenditure to make "good" happen.