Seems like you have more to worry about besides cleaning. Your mom can get outside help, my mom did in my grandmom's final years. Tell her to look in the yellow pages or call her insurance company. My mom had someone come and clean up and feed my grandmom and stay so mom could go shopping or come visit me at no cost to her. She had a few lemons in the bunch and I'd recommend screening prospectives.
With you house-you have to take it a little at a time. First get stuff off the floors. Recycle old newspapers and magazines. I have a lot going on in my own house-20 yrs of hoarding stuff in the basement mostly. I am bringing up a few bags and boxes at a time to go through. I started with Christmas stuff as I had it all pulled out anyway. I have tossed a lot and consolidated a lot too. Plastic boxes are my new best pal. Good luck!

It does sound you have alot of stuff to deal with right now besides the house cleaning.

When my mom got really bad, my half-sister came out from back East and got a Hospice thing set up through her insurance (I think it was thru her insurance). They sent a nurse out and a careworker....they visited 2 or 3 times a week for short periods to give her a baths and check up on her. And the meals on wheels organization delivered meals for my mom. At the last, I had to order a live-in "home domestic aid" to help with the housework and listening in to my mother so I could get some sleep and go to the grocery store. She wasn't a trained nurse and English wasn't her native language so I had some problems with her and my mother's medications, so I had to watch her like a hawk. And she was expensive. It wasn't ideal but it was the only way I could get any sleep and go to the grocery store when my mom got really bad.

So someone needs to do some research on the internet for organizations that could help your grandmother and your mother take care of her. There my even be organizations that will do it for no or low cost, depending on the financial situation of your family. But they don't find you, you have to find them.

As for the house, do a few things items a day...it will make you feel better than doing nothing but won't take too much time/energy. If you need help with motivation (like I do), marking the number of items you do on the calendar can help you see your progress. And then you can challenge yourself to do one more item than you did the day before.