Sounds like it is time to prune! Here are a couple links that discuss how to prune the twig dogwoods. You should fertilize in the spring after pruning.
Welcome! I’m Margaret Roach, a leading garden writer for 25 years—at ‘Martha Stewart Living,’ ‘Newsday,’ and in three books. I host a public-radio podcast; I also lecture, plus hold tours at my 2.3-acre Hudson Valley (NY) Zone 5B garden, and always say no to chemicals and yes to great plants.