Does PEMOMTYP refer to the CURRENT child-parent relationship?

I am interested in an adult’s childhood familty structure. Is there any way that something like PEMOMTYP (or other such questions) can be used to get information about the child-parent relationship while the person was growing up?

Yes, the PEMOMTYP variable relates to the current relationship between the respondent and their mother. Note that because the CPS (and the US Census for that matter) are sampled by dwellings “family interrelationship” variables only apply to family members that are currently residing within the same dwelling unit. That is, children who have moved away from their original home and formed their own household cannot be linked to their parents. So, in order to look at an adult’s childhood family structure you’ll need to look into some sort of longitudinal data set. The NLSY data may be a place to start looking for this sort of data.