Hi! I'm Kelly. I'm a potter like mikomum, and I've given this a lot of thought!
First, look hard at time suckers in your life. If you spend any time watching TV that you could spend at your art, well, that one's easy. If you feel too tired when the kids go to bed, my suggestion is, make yourself just get started. Promise yourself half an hour. "Fake it 'til you make it". Once you drag yourself to the project and get started, you might suddenly find you're getting into it and on a roll. (Kind of like married sex)
Or, head straight for bed when they do, and get up absurdly early with a fresh start, hot coffee and peace and quiet while everyone's still asleep.
Also, consider changing the scale or style of what you do, so you can work it into the life you have. Is there a way to paint small, or in several short sittings? A way to keep materials nearby so you can grab them during naps, or in those unpredictable magic moments when the kids play quietly somewhere?
It's hard to switch gears from life/mommying/interruptions to being able to focus on something creative, but maybe it will be a push into something new and different, like when our prof set a timer and had us sketch a model's poses for 60 seconds per drawing. It looked nothing like my more careful work but it had ... something, y'know? It was alive and kept my brain working, and worked its way into my later work.
I used to take a lap board and a bag of clay on long drives when dh was driving, and make little figures, roulettes, stamps, textured beads, mini teapots, etc. I carried a ziploc with a washcloth to clean up afterward and a diaper wipe box full of bubble wrap to transport my little pots.
Miko, when I was pregnant or nursing (like 7 years of my life) I wanted no contact with barium, lithium, cobalt, manganese, and certainly not mystery commercial glazes or unvented kiln fumes. I took to working with textured surfaces instead of glazes, colored clays and earthenwares, terra sigillatas and Lana-Wilson type stamped surfaces. At first I resented the limitation but those kinds of challenges took me in directions I might never have tried, and what I learned still informs my work.
(Eventually I discovered the book "mastering ^6 Glazes" -- all tested glazes by safety-conscious chemistry geeks, with leaching levels safer than EPA standards for drinking water.)
When I had 3 under 5 I emptied out a linen closet, lined it with tarp and moved in my potter's wheel. There was just enough room for a bucket and a chair and I kept everything dust-free with a fat sponge. I could throw during naps or late at night.
My mom says, "When I look back at my life, the time with little children was just a blink". Honestly, I don't regret a single moment of my life that was spent rocking babies instead of making art. My kids are 8, 11 and 13 now, very independent, and I am homeschooling them while commuting to another state to do an MFA in ceramics.
It all will wait while the kids are little... no experience is wasted for an artist and it will all be reflected in your work one day. But if your life is opening up a little from the needs of babies and you really want to work, you'll find a way.
That's my little pep talk for the day
(my stuff is at primalpotter.com)