How to keep sumac from growing back?

My mom and brother cut a bunch of it down and burned it last week. Needless to say, my mother is an itchy, rashy mess and is taking herself to hospital today. Terrible.
It grows around the shed so either has to be cut down or prevented from growing in the first place. Should we use black plastic and some sort of mulch over a season to kill it off, would sheet mulching with cardboard do it, or should we call an "expert" bearing chemicals? D'oh. This is nearly as bad as when she peed into poison ivy on the golf course a few summers ago. That woman is prone to rashy experiences, the poor thing  .

Remove the roots

Lemme just say, NEVER ever burn sumac/ivy/oak leaves/stems/roots... My cousin just about died a few years ago. They didn't realise they had thrown a log with old brown shoots wrapped around an oak log (even brown olden shoots of ivy still have urushiol in them)..

Go gloves, and identify the root pieces and remove them, or get a goat in on your property.. They'll eat it up.

No duh about the burning, I can't believe they did that.
How to remove the roots? I don't even know what to look for. Apparently she should never go near the stuff again, once sensitized any contact will immediately cause a reaction from what I've read.