Power of Attorney of a child yet to be born?

I was given power of attorney for a child who is not born yet..She is due in 4 weeks..Her mother is a addict and homeless and has no desire to parent the child..She is unsure as to who the father is but the man saying he might be the father also has no problem with us caring for the baby legally..He has already given one child up the same way...The mother and I signed a POA form and had it notarized...Will I have any trouble from the hospital when it is time to being the baby home with us after birth? Should I have the POA papers with me or will they even question whose car the baby get's in? ( parents have no transportation..) Thank you!