In non-nuclear families, the third "parent" is normally an uncle, aunt, or grandparent that can provide additional financial support and babysitting options for the two parents. This is common in many countries where multiple generations of extended families live in the same house or neighborhood.
My in laws live literally a block away and watch our kids multiple times a week. The girls sleep over there sometimes too.
In no way are either of them a third 'parent'. This idea that grandparents and aunts and uncles can actually be a third parent has to die. No one who actually lives in these situations is confused as to who's who.
We lived with my grandparents as children and while again, we loved them very much and they watched and cared for us like parents... The relationship is fundamentally different.
Even without a multigenerational household, there are plenty of American families that rely on grandparents for regular support/babysitting. I don't know how we would have managed our kids without a standing one-night-a-week date night.
