These can be renovated by cutting all stems to near ground level in the spring, removing any suckering shoots that arise around the base of the plant. Or you can remove one-in-three of the oldest stems each year for three years until the whole shrub has been rejuvenated. You may find that both your trees come from one originally. Personally I would prune less drastically because they can sucker quite a lot. Just take each branch back to where you think it looks better and remove any suckers you find. I have to tell you I had one once it suckered everywhere after I had pruned it, never again

One of those plants that should come with a government health warning in my opinion.

Many thanks for the suggestion. We're cowards, and these Rhus don't sound like they will be beaten. I think that we'll leave them as they are for this year, because they are not suckering too much (and they are well away from boundaries & house etc), and when we get fed up with them, we'll cut them down and try SBK or Roundup to finish them off, although it doesn't sound like they give up easily! Shame, they are attractive.