Hard to tell from the picture, but check out Houttynia cordata. Looks similar, but I may be wrong. If my guess is correct allow it to grow, use herbicide - then allow it to re-grow, use herbicide - keep repeating. A plant that should not be allowed.
hortster

I looked up some images of what you suggested and it I don't think that's it. This doesn't flower and doesn't have the whitish leaves (the leaves are red too). Is there a way I can send you some higher res photos? Thanks!

The (unfortunately) popular horticultural varieties, such as 'Chameleon' have hot pink, creamy white, and green leaves. Look at that one. Like I said, pictures are not clear, but sounds like a likely culprit!
hortster

Here is a link that might be useful:

I have a better photo, but can't seem to get the website to let me post a second one. I also didn't mention that last summer we didn't have time to manage them and they grew to three or four feet! Also never any flowers like the Houttynia cordata.

Evil japanese knotweed. Leaves on the young sprouts are often reddish.

Here is a link that might be useful: JK sapling