If I live with my mother, rent free, should I be her only caregiver?

NO, get her and more important yourself help or you will break sooner than she will!

you are providing a solution that your other sibs are shying away from .
i can put it this way ;
two aps ladies came to my moms house ( routine after a hospitalization ) . one of them saw me as a damned sincere person who would protect my mother from anything that came along . the other saw me as a loser parasite living off his mother .
caregiving is a roller coaster ride . you have to follow your heart ..
the non carers are going to hurl crap . they dont want the position , and couldnt handle it if they had it .

Are you asking if room and board is adequate payment for fulltime caregiving?

Then the answer is No.

If "caregiving" means you share your dinner with her after work and help with the housework, then the answer is "Perhaps."

Do you already live with Mother? What are your caregiving duties? Can she be left alone for periods of time? Do you work outside the house?

A little more detail may get you more specific answers.

I was at a meeting today where a retired nurse complained that she had taken care of her grandmother for 2.5 years, had been promised money for her efforts. But when grandma died, the will spread the proceeds evenly among her and two non caregiving siblings. She learned that if she had wanted to get paid, she needed to have a contract in place in this state. Be gery careful about what you get into. It will be worse than you can now imagine.

Paid live in caregivers get wages as well as room and board. Oh, yes, they only have to work so many hours a week and get vacations as well. What your sibs are angling for seems more like indentured servitude to me, but seems like you are the only one that owes mom a debt?

Barb, who is taking care of your mother now as you wrote "if I live with Mother"? What are Mom's health issues?

As for your siblings, its their Mom, too. You all need to work as a team.

By the way, 40% of caregivers pass away leaving behind their love ones. Depending on the parent's health issues, it can be very exhausting work, and you'd be lucky if you get 2 or 3 hours of sleep at night. If that happens to you, would your siblings step up and move in with Mom rent free?

Well, they are wrong in my books. No one decides about your life except you. They don't want the responsibility so want you to take it on so they don't have to. With that attitude I doubt they would be of much help - don't count on them. Other arrangements' can be made for your mum's care.

How much LIFE are you putting on hold? Job? Family? Proceed with caution. Depending on the amount of care she needs you may be giving up your life for many years.