My dog has had diarrhea and has been throwing up. I found pieces of this plant where she hangs out. Can you help me identify it?

Very difficult.
If the dog seems seriously ill, do not wait for answers here.

If not seeming seriously ill,
Look around where she may have chewed it off, maybe find a plant looking chewed and show us that.
Many plants contain irritants, and taste bad enough because of them, that animals don't usually eat enough to be seriously ill.
Be aware this is an entirely voluntary, hobby site and nowhere near as actively used as some big social sites. You may wait a day or more before even having a likely answer here.

Thank you, Sally. My dog has recovered, now, but I am still baffled about the plant.