I don't have children, so I can't really help you there but I do have some things to say about time management in general and motivation.
1. I run because I think races are fun. If I didn't sign up for races, or knew I'd participate in one, I don't think I'd be running. The prospect of signing up for one is enough to keep me going. Right now I'm not signed up for any but I do plan on running a Disney half marathon in September 2017 and that's enough for me to train. There are a lot of bonuses to collect along the way - being able to run to catch the bus without feeling exhausted, seeing my time become better and better each week, etc.
2. Regarding time management, I found out about two years ago that while some people genuinely have zero time for non essentials, most of us, in fact, do. The thing is, your schedule isn't going to suddenly make room for an activity. I think you have to make that room. You have to decide that X and Y are your priorities (and by priorities I mean are essential to your well-being as a person) and the rest will just have to adapt. I'll take my own #1 hobby as an example. I'm a reader. I need to read every day for an hour to feel okay. I'd rather go without food and clothes than without books

That's me. Knowing that, there are some points in my life when my schedule was so packed that just looking at alloted times for essentials, you'd think I wouldn't have had the time to read, but I've always read. I read during my morning commute, during my lunch break, during my evening commute, while running (I listen to audiobooks), while cooking (audiobooks), while showering (audiobooks), while doing chores (audiobooks). For about a year I did my reading from 4 to 5am because there was no other way

Most days, I get in way more than just an hour of reading. I multitask a lot. The one thing I can't do well (but I do it anyway!) is manage two word-related activities at the same time. I can't listen to a podcast and write. I can't work and talk on the phone. I know someone who calls her mother during her workouts so she doesn't 'just talk on the phone for an hour while everything else gets postponed.' The bonus is that she can't get angry at her mother on the phone anymore because she's too exhausted to

What I'm trying to say is that if you're looking at your schedule and at the times you allot to essentials, you're never going to suddenly find a hole in there where you could go run

You have to make it fit by finding a way to change things around

I hope it all works out for you
