First, poverty statistics comparing 1950 to today are more complex than they appear since the marriage rate has dropped a lot. There are more single-income households, so the average household income looks different though income might not have changed all that much.
Second there is a very strong correlation between marriage rates in neighborhoods and poverty levels in the same neighborhoods. Likewise, there is a very strong correlation between marriages in households with children and poverty rates in those households. Very few households with two working partners live in poverty.
It's... complicated to discuss family structure when talking about poverty and child welfare, but it's possible (I would argue likely) that family structure is a key contributor here. In my opinion it's rather foolish not to at least bring it up and consider it.