In your zone, with what you describe, horseradish is quite possible. Other possibilities are comfrey, dock, or burdock. Identifying it would help somewhat. Have you ever seen it flower, and if so, whassit like?
The general recipe by which you can eradicate almost* anything, given 2-5 years of consistant work, is: any time any of the plants gets more than 4" tall, mow 'em down or better yet go out there with a knife and cut the top off as deeply into the soil as you can reach. EVERY TIME they get to that size, EVERY PLANT (some of these buggers are connected by underground roots). Without fail. It takes time. It does do the job, though.
(*-except goutweed aka bishop's weed, or comfrey, or horseradish, or a bunch of grass type weeds.)
Good luck, and post pics if you can,
Shellie, yes, bishop's weed is EVIL EVIL STUFF, and there is probably no way of getting rid of it in your mother's garden without COMPLETELY smothering over the entire area for a number of years. I have heard that digging up and replacing the top 6" of soil, followed by heavy mulch (that you can plant real plants thru) plus regular use of Roundup on every single sprout of bishop's weed that appears, will keep it well controlled. But it's work
Pat, who is openminded towards weedy, spreading garden plants in general, but will never have goutweed (however pretty and 'useful' the variegated form is) ANYWHERE near this place, because, eeep.