Kousa dogwood die back and Cornus Florida wilt
Last summer I lost a large American Elm which provided partial shade to both a Kousa Dogwood and a Cornus Florida. The kousa is dying back from the top of the crown down to the lower branches. The leaves at the top of the tree (24') are stunted and the twiglets are bare. The branches near the base of the tree look wilted. The nearby Cornus Florida has leaves that look very wilted (although they are not yet stunted). They hang directly down, rather than out from the branches. If we had not had so much rain, I would assume they were parched.
Removal of the elm should not affect these plants unless the stump grindings were spread/piled around the dogwoods. But it would make the area wetter, because the elm is not absorbing a lot of the rainfall.
Drooping (wilting) leaves and stunted top growth/tips points to a root issue. (If it was a big problem with the trunk, but you should be able to see that and, besides, it would probably not be on two separate trees.) Root damage can be because of drought, as you mentioned, put also from too much water. Both kill roots.
We may be able to be more specific if you send us photos of the base of both trees.
There are several other abiotic issues that could be affecting your tree here: http://extension.umd.edu/sites/extension.umd.edu/files/_docs/programs/hgic/HGIC_Pubs/Landscape/HG201...