It's a Grewia, also called Lavender Star Flower.

There's a big thread in the Weeds forum pertaining to bindweed...you might want to search for it. I read on that thread someone had success getting rid of it by gathering up some of the foliage (still attached to the roots in the ground) and immersing it in a container of Roundup. Make sure it's protected from rain and stable so it doesn't tip over. Yanking it out won't really do anything...the roots can travel very far.

Looks like a Sedum, maybe S. rupestre. If so, a full sun plant, creeping ground cover that shouldn't need any watering except in case of serious drought, hardy to Z4. http://davesgarden.com/guides/pf/go/3294/

we are in eastern Mass, but not sure if considered "sandy" part! If you mean along the shore or down near the Cape, then no. About 25 miles southwest of Boston. It does seem bent-like, and I've almost always had tufts and patches of bentgrass (the bane of my existence in what is otherwise kbg, rye, fescue mix) and this seems way more aggressively vine-like. While the other bent patches are carpet-like, this one is more like a clump with 1 definitive vine. The clump in the picture is just one that is lonely in the mulch bed, but the lawn itself near this area is a whole big patch of this stuff. Thank you!