So stumblest on my counsel?

I'll start by acknowledging the first rule of parenting advice: don't give unsolicited parenting advice. But since you're here (of your own volition?), let's also recognize an important metric for advice: relevance. Somewhere along the spectrum from "too generic to be of significant value" to "too specific to apply to my unique child/situation" lies a sweet spot of relevant advice that is genuinely useful and applicable to your audience. One size does not fit all.

With that in mind, my quick advice for new parents leans generic and won't likely strike anyone as the missing piece of the puzzle, but it does serve as pretty good "try not to forget" material. Let's get to it already.

Parents are role models.

Children learn from watching us. The next time your children are pushing you, remember that they are observing (and learning from) how you react and respond to their drama. Your job is to lead by example.

You hear more when you listen completely.

Are your children nearby? Eliminate distractions. Give that phone a break. Engage. Connect. Listen, and learn.

Teams accomplish things that individuals cannot.

Regardless of how awesome you are, you can be greater with the right help. Foster and nurture the social superorganism that is your team, and consider that your team may be larger than you realize. Yes, you have an inner circle, but don't limit yourself. Your network is your team.

Isn't this common sense?

I thought I already knew and understood these principles, but knowledge is not enough. The real benefit comes when we act on those principles and exercise the self-discipline to overrule negative impulses.