I did learn last night that this has been a problem with this particular plot of land for quite some time. I have honestly never seen weeds like this. After being incredibly stressed about it for a few weeks, I have have come to terms with them.
I will do what I can, and hope that the garden plants take over as best they can. I can create a mountain of pulled weeds daily, and every time I go out, they have multiplied once more. It's frustrating and infuriating, and my child won't play on his own for the amount of time needed to deal with the issue, and frankly, I'd rather be playing with him!