How can I write, when I have no privacy?

Dear Literary Ladies,
I want to write, but my circumstances are less than ideal. My kids run around the house, and someone is always interrupting me. I have no private space, let alone what Virginia Woolf called "a room of one's own." Were any of you in the same position, and if so, how did you do it?

During long years of struggling with poverty and sickness, and a hot, debilitating climate, my children grew up around me. The nursery and the kitchen were my principal fields of labor. Some of my friends, pitying my trials, copied and sent a number of little sketches from my pen to certain liberally paying “Annuals” with my name. With the first money that I earned in this way I bought a feather-bed! for as I had married into poverty and without a dowry, and as my husband had only a large library of books and a great deal of learning, the bed and pillows were thought the most profitable investment. After this I though that I had discovered the philosopher’s stone.

So when a new carpet or mattress was going to be needed, or when, at the close of the year, it began to be evident that my family accounts “wouldn’t add up,” then I used to say to my faithful friend and factotum Anna, who shared all my joys and sorrows, “Now, if you will keep the babies and attend to the things in the house for one day, I’ll write a piece, and then we shall be out of the scrape.” So I became an author, —very modest at first, I do assure you, and remonstrating very seriously with the friends who had thought it best to put my name to the pieces by way of getting up a reputation . . .

—Harriet Beecher Stowe, from a letter, 1853

A note from Nava: Harriet Beecher Stowe had seven children, and was the ultimate working mother—she was compelled to use her pen to augment her husband's meager salary, writing sketches, poems, essays—anything that would yield quick payment. All the while, for many years, she burned to tell the story that scholars agree aided the cause of abolition tremendously—Uncle Tom's Cabin, and finally did so at age 39.