Can I pay my sister for sitting with my mother at nursing home?

Jeanne is right that you should consult a lawyer if Mom is likely to go on Medicaid in the next 5 years.

I think it's great if your sister wants to spend time with Mom to ensure that she gets good care. I hope it takes a burden off you and the rest of the family. Caregiving isn't like chopping wood. You can't "simply" divide it up equally. Each person may contribute in a different way. I wish you all well.

Of course you can pay her with your own money. I take it you are asking about spending Mom's money on this. Who might object? Are there other siblings or relatives? Does Mom have enough money for this to go on indefinitely?

I assume that Mom is now self-pay at the nursing home. Is she likely to be able to continue that the rest of her life? If she might ever need to apply for Medicaid they will look at how her money has been spent in the previous 5 years. If this is a possibility I'd consult an Elder Law attorney and get it set up so that the money to your sister does not look like a gift.