I think the trend is probably there in certain circumstances, but there are a couple of issues I didn't consider enough:

1. Most of the parents I was thinking of are parents of very young children, and as children get older other issues come into play with parenting styles.

2. I was kind of assuming favorable Socionic relationships and that's just too big of a variable.

So in the circumstances where children are very young and the relationship is favorable, I think there's something to it, but there is too much else that goes on as kids get older and depending on the Socionic relationship.

Thanks to everyone for your experiences and I hope more people share!