I would suggest you buy this book.
How to Protect Your Family's Assets from Devastating Nursing Home Costs/Medicaid Secrets 2021 Version by: K. Gabriel Heiser, Attorney
If you buy this book from anywhere, make sure you buy the most up to date version. Many sellers are selling old versions from years ago. They will be out of date for the new laws and rules. This book seems to be updated each year so you might want to wait till 2022 to get the most recent version. The book is not cheap but well worth it.
I bought this book and have the 2014 edition. It is very well written and easy to understand. If I were you, I would read this book and have a notebook to the side to jot down all the pertinent information related to you and your mother. Plus, have some post it tabs to stick on pages you want to review. Once you have absorbed what the book says, then see an elder attorney and ask all the questions. After reading this book, you will have a greater understanding on what you can do and cannot do.
My Mother passed away and didn't end up staying very long in a nursing home. Medicare covered her short stay. Reflecting back on things my Mom and I should have done at minimum would have been to put me on the title of the house as a joint owner and same with her car. It would have made probate a little easier. However, I was an only child so probate went pretty easy and the judge allowed me to sell the car and house right away. The one smart thing we did do shortly before she became very ill was to put my name as joint owner on her IRA's, checking accounts. That made for an easy transition. One of the hardest thing was some of the stocks Mom had. They were in paper certificate form and the companies names had changed over the years. I had to mail them to the companies and eventually they were sold and I received a check for the value. I had to send death certificates to the companies with the paper stocks.
Your mother may never go to a nursing home and many people who are very sick don't live very long in a nursing home. It was one of the darkest times of my life to see my Mother in a nursing home. Wishing you and your mother all the best.