Answer: Moving a tree that is distressed just adds addtional stress and may even kill it outright. Based on your description it is difficult to make a suggestion.
Although dogwoods do prefer an evenly moist yet well drained soil they are often found in the wild growing along the edge of oak woods in competition with other trees. They are also often grown successfully in full sun under landscape conditions especially if provided with supplemental water under drought conditions or during especially dry spells.
These trees are very difficult to transplant successfully so unless you have a very good reason to try to move it I would probably recommend against it. They are fairly shallow rooted so you will not need to dig terribly deep; you will however have to dig very wide because a tree's root system often spreads beyond its branch span.
If the tree seems to be in trouble, you might want to consult with your County Extension (336-4034) as to what the possible causes might be and what you might be able to do to help it apart from moving it.
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