TL;DR - I'm successful in my dev job and family life because I have learned to write everything down, set parameters for the things I do, and have surrounded myself with positive people who care about me and my family. This combination of factors results in spare-time to learn new skills, exercise old ones, and my company allows me to experiment.
-- The Whole Story --
First, a little about my current, professional role; I'm one of 3 backend/web developers and the primary dev for our flagship i/e enterprise offering. I don't deal with architecture or design unless I request to do so. I am responsible for writing the majority of our tests, choosing and implementing the tools we test with, and participate fully in code-review, QA, and bug reporting/fixing. Like many devs, I attend weekly meet-ups, code side-projects, and do my best to stay abreast of developments in, well, development.
Personally, I have 2 children, 1 of pre-school age and the other in an early elementary school grade. I'm able to -
* help my oldest daughter with homework
* attend school functions
* pick them up from daycare often
* do activities, like dress-up, painting, and building forts
* each night: give them baths, read them bedtime stories, and sing them lullabies
Our sitter, a family friend, recently asked me "how do you do it?" and followed up with "I'd be exhausted!" Her question caught me off guard. I don't necessarily think I'm doing anything special. In fact, I often find myself worried that I'm not doing well enough. Luckily, there are people like her in my life who remind me that I, and my wife, do a pretty damn good job.
-- How is this possible? --
Well, for one, it's because of people like her; the people in my family's lives who care about us. Another contributing factor is the company I work for, an organization that actually cares about me. Our team is willing to pick up the slack when a member needs help. Being based in Chattanooga makes a difference, too, and although commute times can reach ~45 mins, it's a fairly low ceiling, especially when compared to SV commute times. Lastly, if you work on a team, and that team doesn't give you the opportunity to grow your own skill-set within your professional-role, then that team is failing you. There's a reason that professional athletes are given access to training facilities and musicians are allotted time for rehearsal; you need to exercise your dev muscles. If it weren't for my team sometimes giving me the opportunity to explore rabbit holes, and knowing when to pull me out, I wouldn't be half the dev I am today.
PS - yes, when you first become a parent, your education/productivity/effectiveness takes a hit; that's just how it is. Otherwise, you'd be leaving your significant other/partner to do it all, and I've seen how that can affect a relationship. It's important to acknowledge this drop-off, plan for it, and make up at least a portion of that lost ground over time.
Good luck!