I was arguing about the effect on GDP, where "not having to pay for child care" appears as a negative effect, a smaller GDP.

From a GDP-maximising point of view, it's better for everyone to contract out every aspect of their household than it is to do it themselves. An economy built on taking in each other's washing has a much higher GDP than one where each does their own. Stepping back from GDP makes that look nonsensical.

Is reward the same as not being penalised? I don't feel that's true.

Aren't you missing a variable for the cost the unskilled woman pays to have someone watch her children while she's being paid to watch the skilled woman's children?

You're ignoring the value the children bring to society by growing up and entering the labour force themselves. The highly skilled woman making a lot of money is unlikely to have her child make significantly more than her (regression to the mean).

On the other hand, empowering an impoverished woman to provide higher quality care for her children will significantly increase their upward mobility.

The highly skilled working mother can only spend less than (1 - marginal_tax_rate) * (1 - employer_profit_margin_on_labor) * $X on an hour of child care.

It was this exact calculation (and a high marginal rate) that led my own highly skilled wife to conclude that it wasn't worth working when we had our second child.

Do you have children? By what stretch of the imagination is caring for children an activity best performed by unskilled individuals?