dogwood tree and shade
by Angelica
(Redford MI USA)
Doug says that dogwoods are fairly shade tolerant. Euonymus bushes are sun-lovers and will tolerate some shade. So it depends on what kind of tree you intend to plant. If you're going for a dense shade tree such as a maple, then yes, when it gets large enough, it's going to shade out and kill the other plants (but not for quite a few years).
If you plant a more open, less dense shade producer such as Birch - then your plants are going to grow better but you won't get the same cooling effect.
So the answer to your question is that "it depends" on how much shade you're going to produce with your choice of tree. In any case, it will take over 10 years for that tree to get tall enough to do any appreciable damage to the larger Dogwood.