What is this plant and how do I kill it! Please. I have dogs too so a natural remedy would be nice.
This looks like goutweed, aka bishops weed. Aegopodium podagraria. It spreads via white, fleshy underground rhizomes. To my knowledge, there is no "natural" remedy. You can burn it with a blow-torch device but it will come back. Re-treatment will be necessary and it may take several months or even years to be rid of it. Other options are to cover the area with thick black plastic and let the sun kill it (solarization) or cover it with an outdoor carpet. However, it may pop up just past the edge of your treatment area. If it is coming into your yard under a fence, you will not be entirely rid of it since it will creep back into your yard. To see it, do a search for "garden blow-torch".