Revenge of the "mother" weed

We called the pricklers when I was growing up, I'm pretty sure what I have is from the thistle family. My neighbor and I firmly believe that there is a "mother" plant somewhere between our two yards. The "mother" plant grows wild under the earth, sprouting her babies in our lawns and flower gardens. I have dug and dug and dug, seriously down 2 feet, to get to the "root". Last year I went after her with a vengance. Before I planted one annual or new perrinial...I dug up my entire flower garden. I moved the perrinials I wanted to keep, into buckets of soil, while I dug into the ground to find the "mother". I found teeny tiny tenticles, resembling fine hair and blasted that with weed killer. Next I put a product that prevents weeds from coming up into the soil. I replanted my perrinials, planted some new annuals and thought my job was done. But no, I was wrong. She's back and with a vengance.

Any ideas on how to kill this "mother"?