I think the first is wild cranesbill (wild geranium) and the second may be one called Clasping Venus's Looking Glass, Triodanus perfiolata. It's a pretty little wildflower, and the cranesbill, while it will fill lots of space, is easily thinned and pulled if you have too much of it. Nothing to worry about.
http://www.wildflower.org/plan...
and
http://www.wildflower.org/plan...
I think this is the one we have, Geranium carolinian:
http://www.wildflower.org/plan...
(I'm also in Richmond.
)
See pics at the links for comparison. What do you think?