This is just a suggestion, but I've worked in healthcare human resources, so I have a bit of background in wages.
*You could check with local home healthcare services
and see what they pay employees (not what they charge a client) for the kind of care your mother-in-law needs (just basic bathing,feeding, toileting help, or medications and more skilled care). They may not want to tell you, but there are ways to find out. Turn on the charm! Do you know of someone who might know someone? Without that number we have nothing to go on, but there's more than one way to get the imformation. If you can't find out, let me know by posting here. I'll check my sources and we can adjust it for the cost of living where you live. Or I can get an idea of what the agencies charge compared to what they pay employees, and it's easier to find out what they charge.
*Use that as an hourly rate.
*The other hours would be considered "in house on call," which is the term hospitals use for shifts where a care provider has to stay in the hospital and be available at a moment's notice. Figuring that rate will be guesswork, I think. It could be figured as a percentage maybe 10-15%, just guessing) of the hourly rate. A hospital human resources department might be able to help, but I think all the employees who work in house on call are salaried, so hourly rates don't apply.
*Then you would estimate how many hours a week you actually care for your mother-in-law or do things specifically for her ( prepare special foods, go to the drugstore, talk to the doctor, do special laundry). That would not include time you spend together watching TV, talking, eating. Obviously that will vary, but you could average it over a few weeks.
*For those hours you would be paid the hourly rate.
*The other hours of the day you could consider in house on call, and get paid whatever percentage of the hourly rate you decide for that.
*Another thing to consider is that the amount of care your mom-in-law needs will increase as the disease progresses, so whatever hours you figure as work versus on call will need to be recalculated now and then. I'm thinking that sometimes it may not change much in a year, other times it might change rapidly. Who knows? That part isn't as important as getting started and realizing that parts are subject to change. The hourly rate will change over time, but you probably only need to check on that every two or three years, maybe longer.
*I've probably made this harder to follow that I should have, but it makes sense to me and I know nothing about math! Again, this isn't based on any information except basic wage and salary principles. I'm sure there are other approaches you could take. On the other hand, this plan is totally logical.
*Are there family members, or maybe a clergyman or attorney, with whom you can discuss this? That might give you a feel for whether it seems fair. My guess is that it will be higher that you or they might have guessed, because it is a huge job! I also guess that no one else will have a better idea, unless there's a secret out there that no one is telling.
*If anyone suggests that this is too much pay, you might gently encourage them to check into home healthcare services. The way I thought this through, you will be getting far less that hiring round-the-clock care. Besides the time you put in, no one can put a price tag on the love you will give your mother-in-law.
*I'm interested in having feedback from others on this site. Does it make sense? Am I overlooking anything?
I wish you all the best. You are doing a wonderful, extraordinary thing. My great-grandmother on my father's side probably had Alzheimer's, but it hadn't been given a name then. My mother cared for her for many years, and I was still a child, so I know what sacrifices you are making. My husband was diagnosed with Alzheimer's several months ago, so I'm envisioning myself being in the same situation. No one loves him as much as I do, so I'll be caring for him as long as I can.
!!!Hold on! I just thought of another way to go about this! In some states, a relative can be given brief training in care, then the state actually pays the caregiver a wage. I'm sure it's for situations where there are scant resources and the relative can't afford to leave her job to care for the person. Then it's cheaper to pay the relative than to pay for nursing home care. You might check to see if your state does that and find out how they decide on pay.
*My gosh! I got started here and almost wrote a book. Once in a while my mind takes off like this and I have no control over it!
Again, my best wishes. I'd love to know how you resolve this. God's blessings!