Will any legal rights be left after mortgage is satisfied&quit claim is signed?

We have lived in a home for 13yrs and have paid for every payment on a 15 yr home equity my father-in-law took out for 60,000. We have struggled and repeated asked for their help because in the verbal agreement 14 yrs ago, we were suppose to get mortgage and pay them an additional 20,000. Making the purchase price for house 80,000. The problem is the house has been a money pit so we've never come into the ability to clean up our credit and get mortgage. now we have no credit which is almost as bad as bad and last year the mortgage company paid our taxes which we had let roll over for 1 year. We paid every year and would've paid both years before the tax roll was due but because they paid it. we owe them 8400 more and they want it in 12 months. so our payment went from $556 to $1648 a month, 1700 with late payment which we have been unfortunately so know dads mad doesnt care that we can't get mortgage for 12 months because we have no tradelines and is threatening eviction. If we could manage to pay off the remaining $20,000 we owe to mortgage co, could he quitclaim the house with out having any more legal rights on it?It is a sad state of affairs but would appreciate any advice you could share. We are in NY.