Neither would have her husband been counted in the non-farm labour force survey. Thus swapping husband for wife would not have shown up as a change in the first place.
This is an interesting discussion. I remember my economists professor talking about how in Alberta during the 2006 boom labour force participation dropped as wages increased. In that case it was an example of the in-elasticity of labour demand.
From the social aspect it was an example of how for many families 2 working parents is not optional. A situation was fully true earlier in the industrial revolution. As the revolution progressed and labour had more negotiation power over capital real wages rose and duel working parents decreased.
Thus my pet theory is that the reduction in real wages is a non-trivial driving force for the current historic high labour force participation stats.
I'm not sure what you think this proves. When the choice is "do something or starve" people do all sorts of things they would rather not do, from farming to prostitution to selling their children:
https://rarehistoricalphotos.com/4-children-sale-1948/
There but for the grace of god went your mother.