I have temp custody of a child. Baby was placed with me right from the hospital. Mom has had previous children placed with family and has lost parental right to those 4 children. Mom has a history of drug use, prostitution and larceny. Dad has a criminal past, very large, over 4 domestic violence charges, 1st degree sexual assault charge and many other assault charges... there is just to many things to list for dad. Baby is now 2 months old, parents are doing what they are asked to do by DPS, My question is, based on their past will the courts think they are unfit parents?

parents are doing what they are asked to do by DPS,

This is the key point. Apparently DPS has not ruled out their getting custody. They have placed requirements that the parents must fulfill to do so. They would not have done that unless they felt there was some redeemable qualities. So IF they do fulfill all the requirements, then DPS may agree to allow them custody.

Their past , if that was all there was to look at, they would not even have the child now.

And past errors are make them suspect, will not be the final thing, If they are now clean, not using drugs, have followed requirements of the court ( perhaps parent class, perhaps drug programs) and so on..

So the court will look at this to see if they have changed and are now able to raise the child.

Yes these can be used against them, but many courts will want to look also at current situation also