Second the Carolina horse
nettle. Used to do clean up work of areas with a few hundred goats and sheep and found this often on mis-grazed or disturbed
land.
You will have a large seed bank of this in the soil, as you can tell from the clusters of seed laden fruits. If you do good rotational grazing with high densities and quick movements the goats can tank mix this in with other forage and do fine. Work through a strip with it, and then a strip out of it. Poison them a little and leave, the goats have the largest liver:body mass ratio of all of our domestic ruminants and can usually handle it pretty well with a little management.
Frost seeding in a tall medium red or ladino clover and proper grazing rotation will really reduce it. I found it most on clay slopes that had erosion paths or damn-thin grass from chronic set-stock grazing turning clays into surface level hardpans. Toss on a pound or two of radish seed, turnip seed, or swede seed to help break up the hard pan will really help reduce the presence of night shades in the mix. Reduce the sun and piss poor hard soils it loves and you can reduce it to reasonable in no time.
I could plant
enough enterprise and Priscilla apples on that micro climate to keep us all happy from the squeezin's. What a great looking property!