Our yard is in bad shape and completely overrun by these (now) tall weeds. With two toddlers, and bad back troubles, these weeds have spread and grown.

I've tried removing them manually at the root, not only is it taking me forever but I'm wondering if i'm spreading seeds and making things worse. On the flip side, I can use a weed wacker but won't they just come back?

Can anyone identify what these are (pic attached) and what I can do? Getting desperate here! : )