Answer: The roots of your rugosa's seem to have found a plentiful suppy of moisture and nutrients. As long as you feed and water your lawn, the roots will continue to grow toward the turfgrass. You can continue to cut off the shoots as they appear, or you can dig a deep trench between your lawn and the roses and place a barrier in the trench. Dig down 8"-12" and place a sheet of black plastic or weed barrier along the soil from the bottom of the trench to the soil surface. Or, if the roots are really hardy, place a sheet of fiberglass in the trench. This will keep the roots where they belong instead of in your lawn.
You wouldn't want to treat the invading roots or shoots with chemicals - anything you use will be transported back to the rest of the plant!
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