what you do is a carefull application of herbicide, cover everything you want to live with a washable sheet or tarp, spray the offender, and then repeat the next day, on application generally doesn't kill the roots, but two should do it if its strong willed, this is what I did to kill my Ivy in my garden, and I didn't even hurt the larger plants. the reason you don't just pull the stuff is that spraying them kills the roots as well as the plant
Good luck