Dad said I could keep his share of the sale of the home. Is that legal?

It is not likely to be illegal or unethical, but it may not be the best way to handle it, especially if Medicaid may be involved down the road. Do see an attorney who specializes in Elder Law, and set up an arrangement that makes it clear Dad is paying you for room and board (and possibly care).

There would be nothing wrong with your dad paying his fair share of household expenses, you could develop a rental agreement to that effect. Or, if you provide care for your dad, have an attorney draw up a care agreement before you take a dime! Regardless, talk to an elder law attorney especially if there is a chance that Medicaid will become necessary for either your mom or dad. Since there was a split two ways of the house sale, it seems like there should already be something in place.

Once your mom passes away, your dad may need long term care at some point too.

NO. Pay for the nursing home care. The money will be used up quickly. If you need Medicaid and they see you got half and didn't use it to pay her bills, she will be out in the street, because they will not pay until you pay it back.