I'd turn it into a patio with pavers. :)
Then place plants in large pots so they don't have to compete with the trees for water.

But you have to consider:
How far away are these trees from the area you want to work on? Are they actually in the area or are they further away and cast shade over it?

You wouldn't want to install a patio right over the tree roots, which could possibly kill the trees.

Perhaps a photo would help us see what your dealing with?

Horseherb. Calyptocarpus vialis. Native ground cover. Dry shade. Cute small yellow flowers. What more could you ask for :-)

Be sure to read about it, some people consider it very weedy, others love it.

Teri

Here is a link that might be useful: Horseherb

ajuga looks great with horseherb and spreads well to cover. Mine is in dry shade too. Turk's cap will even bloom in those conditions.

Turn it into a mulched or gravel area with ornamental grasses. Available in both low and tall types, you could mix them with shade perennials for a beautiful garden. Many ornamental grasses do well in shade. Very little work is required for this type garden and it looks good in winter too.

I have horseherb and it is dormant much of the summer and winter and this year did not recover for spring or fall either.

My mom considers horseherb 'a terrible weed'. It survived green as could be in her yard, and was even looking greeny the last time I was there a few weeks ago. She lives on blackland clay. The horseherb is establishing itself in bare patches in her yard,just like the mondo grass is doing, sun and shade. My mom however WATERS her yard. I had thought the horseherb might look pretty with ajuga, which limps along in my yard... because I -don't- water it. So ymmv. I'm trying to get the horseherb established with the ajuga.