Thanks for warning us. Sorry it's turned out to be so troublesome. I live in a very rural place where I guess you could say the weeds are invasive, it's not possible to get rid of them, but I can keep them at bay by blocking out the light with something heavy, like boards, or very thick black plastic with chunks of broken cement over the top or at minimum of a shovel's depth of dense, wet straw with boards and blocks.
I mow the weeds first, as close to the ground as I can get, then block the light, but the heavy part is what speeds it up. In just a few days they will get all pale and smashed. It would take weeks to knock them back somewhat. If the greens can't get light they will eventually slow down and hopefully die back. If they were weighted all winter it would be more effective.
But I was just thinking, I have this great little clover ground cover that I encourage because of its ability to fix nitrogen, and it has great little flowers that the insects love, and I leave it, but dig out a small place to put transplants in, and leave the rest in place.
Do you think your vegetables could grow surrounded by the peanuts? Maybe they will be compatible. keep the greens pulled so the peanuts do not shade everything else, but dig out the planting area, don't just pull the greens. Then very densely mulch with straw or hay on top of the peanuts, blocking out the light, but not over your vegetables, just around them.
The peanuts are fixing nitrogen, which is good, they are a good crop? You didn't say whether you liked the peanuts? Is your soil nicer with them there? Are there more worms?
"Life flows on within you and without you"...George Harrison
Coastal California, USA, Mediterranean climate - no summer rain, a little frost mid-winter