Can a nursing home insist I sell a 17 year old car my dad sold to me for $1

If it is your father's second car (he can keep one), you must reimburse him for the fair market value of the car.  An uncompensated transfer is a gift.  If made within five years before the month in which your father entered the hospital/nursing home, it is seen as an attempt to qualify for Medicaid by benefitting family at the expense of your fellow taxpayers.  Remember: none of us ever paid into a Medicaid trust fund.  The money comes from general tax revenues.  Pay the fair market value of the car.  If that increases your father's assets above $2,000, use the money to buy things which he will need in the nursing home.  Many people buy a recliner, television, phone, slippers, socks and decorations or storage units.  Others prepay for services.