I would like to know if I could sell my mothers house and land, and she resides in a nursing home. The land deed is in my mother and fathers name, and he has been deceased since 1984.

Not without her permission. Living in a nursing home doesn't change her ownership rights. If she is no longer has her mental capacities and you have been awarded the control of the estate, then you might. Is their a trust? Power of Attorney? Other siblings?

Seek out a real estate attorney for specifics in your area/state.