I planted one of these a couple of years ago in a shrubby border but it was always sickly so I cut it down to stump level. This year I noticed a few shoots coming through, then a few more. I'm now being overrun! I've applied glyphosate to the shoots, which seems to kill them off but they are coming up faster than I can spray them. That was in the border, they are now springing up in the lawn where I can't kill them. Any tips on how to eradicate this pest?

Rhus typhina 'Staghorn Sumac' spreads by underground root shoots. You may need to dig up the entire root system. Including the runners.

Digging up all the roots is not possible because in places it has gone under a concrete path. Is there a chemical solution the kill off these roots?

Round-Up. If there are roots in areas you cannot spray, wear rubber gloves & rub the chemical onto the leaves. This should give complete root kill.