My name is Naomi Kritzer. I have five books out, and two young kids at home -- Molly, who's five, and Kiera, who's three. I started writing seriously several years before having kids (and started writing back in middle school) but my professional writing career has overlapped heavily with my parenting. I sold my first novel on my older daughter's first birthday. I got the contract for the trilogy I just completed at almost exactly the same time that I found out I was pregnant with my younger daughter, and scheduled my book deadline accordingly. (I turned in my manuscript a month before my due date.)
Parenting definitely makes some self-promotional activities harder. I couldn't go to WorldCon when I had a baby due two weeks later. I couldn't leave my nursing toddler overnight, so any out-of-town cons I attended required that the whole family tag along. (My husband doesn't go to cons for fun. He'll do it to help me out, but he can think of much more appealing ways to spend Memorial Day weekend.)
I did a bunch of self-promotional things early on. I did a lot less for the most recent book; they're a time suck, I was busy, and I really hate some of this stuff, so it's easy to find excuses not to do it until it's too late anyway. I like going to cons; I like blogging (though on my personal blog, I mostly write about my kids); I like doing readings and signings, especially locally where arranging a signing at Uncle Hugo's is just a matter of calling and asking what weekends are free.
(As a side digression, let me just note that I love the two big local SF/F bookstores, Dreamhaven and Uncle Hugo's. They are amazingly supportive of local writers. They host signings and readings; they sell signed copies of our books by mail order; Dreamhaven will send an employee to off-site readings with a box of books to sell. They rock.)
I don't know. I've seen writers make themselves bestsellers through self-promotion. I've seen other writers who had awesome self-promotional ideas that didn't seem to translate into book sales. It's enough to make me throw up my hands and say, "Okay, screw it. I'll write what I want to write, and if it sells, it sells. And if it doesn't, I'll take up writing cookbooks, or juvenile non-fiction, or something totally different."