Its Burdock - Arctium lappa

And yes, their seed pods are called burs. They were actually the inspiration for the invention of velcro.

There are a few things you can do to get rid of it.

1) Get rid of all the burs, burn them or throw them away, otherwise the seeds inside them will spread and you will have a lot more next year

2) Learn to recognize the 1st year plant and dig them up. Burdock is a biennial, so there is no point to digging up the plants after they have gone to seed, since they are dead or dying at this point anyways.

Here's a pic of the 1st year plant http://www.wildpantry.com/images/burdock.jpg
You have one visible in your first pic, on the left

3) Learn to recognize the plant in its second year of growth, and dig it up before it flowers and goes to seed.

Here's a pic of a mature 2nd year plant http://www.horizonherbs.com/images/burdock-seeds.jpg
they can grow over 6 feet high

Here's a close up of the flowers http://www.raems.com/edibles/burdock2.jpg

Their roots are big can grow pretty deep (sometimes over 5 feet) so it will be easier to dig them up the younger they are.

Sorry I can't offer any 'chemical' solutions. I don't use those types of products because I use Burdock as food and herbal medicine. In case you're curious check out http://www.pfaf.org/database/plants.php?Arctium+lappa

Sorry about your dog Those burs are really nasty to animals, little girls' hair, socks and sweaters.