A right way to live with children is of course different from without children, but I don't think the two are incompatible?
In fact, I think having children is helpful in improving your own attitudes, because it can be really put you to the test.
I also think it can be helpful to have some kind of idea of what being a good human entails. For instance, instead of yelling "Don't do that!" I sometimes manage to ask "How does X look like? Are they happy?"
Of course, one must respect that children have their own lives and are starting afresh - the set of values we've determined for ourselves isn't necessarily something we should interpret too strictly in the context of a child who hasn't yet had the chance to experience the world.
"So it goes"
Just as a stab in the dark, perhaps you perceive the philosophy of stoicism as being orthogonal to a healthy amount of flippancy in life? If that's the case then I would make the case that the two concepts aren't actually mutually exclusive.
The main failure for the Roman empire was that he failed to name a successor worthy to the task, so Commodus got the gig. I don't know what his failures as a father were or were there any but Commodus came out just wrong either way.
Either this teaches us one of two things or both: 1. even a wise sage is unable to heal his family or 2. Stoicism does not grant you universal wisdom.
Either way, the outcome is that stoicism is obviously not a universal remedy.
If you read Marcus Aurelius' Meditations, the take out message is that the world is shit and people are horrible, but that is no reason not to behave as a gentleman and carry yourself with dignity.
Stoicism can be applied by personal choice to various situations in ones life, but it's hard to make it into a socially pro-active philosophy.
And yes, I generalized whole lot of stuff based on one example only. Call me bayesian.
Your story reminds of people pointing fingers at misbehaving children of kindergarten teachers.