A thick mulch that shades out the foliage below will kill plants, but more likely some will stick up through the mulch and keep going. This is more likely with the English ivy, but if you had shade and now have sun on it the ivy should really suffer some sunburn.
Trees can be planted there, in fact a multitude of species will tolerate such conditions. Some that are good choices include Chinese (also called Lacebark) elm, Willow Oak, Tulip Tree, and Dawn Redwood.
Check out the following web site for lots of great suggestions:
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