Answer: Coppicing is an okay procedure, especially in woodlot management, but I'm not sure why you'd want to perform such a procedure in your garden. The idea behind coppicing is to produce what we term sucker growth from the base of a tree, specifically so we can harvest the wood and manage the density of the woodlot. While your yellow twig dogwood will respond by producing lots of attractive stems, Rhus and cotinus may end up looking like they've had a bad haircut! I'd forego the drastic pruning on these plants and allow them to develop naturally.
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