lol! I don't work full-time, as such. I'm a registered carer for my youngest (special needs child), and my eldest is at home with us (home educated) but it's not in the same league as full time work + kids. Or maybe it is, I dunno. I have no basis for comparison, after all!
The same general philosophy applies, though. The baseline truth is that you won't be as productive as someone without kids, in all probability, and that's okay. It's not a race, there are no prizes for finishing a manuscript two months sooner or later.
Try to have small, achievable goals that can be achieved in a relatively short timeframe. Things like: I'm gonna work on finishing this chapter. Don't worry about the whole book, or the whole story; tackle one section at a time. A lot of writing is a psychological chess game played against your own brain, and consistently hitting small goals will feel like progress, while helping you be more productive/keep your spirits up.
Don't wait for the perfect moment; it's okay to write while tired or distracted. That's what revision is for ;-) and later, beta readers to catch your tired-parent-brain mistakes. Don't expect perfection, and accept that you're writing under constraints.
I also like to do as much pre-writing work in advance as possible. When I'm not sat down typing (which is most of the day) I spend a lot of brain-power thinking through my scenes, and arranging them in my head. That means when I do sit down at night, I'm usually ready to go and can get things down on paper.
The tricky one for me is taking time to read and crit. Those are vital to writing, but it's hard not to feel like I'm "wasting" writing time. It's never a waste, though. And neither are breaks, or time spent exercising/relaxing.