looks like the neighbor wants a fence to keep you out.  it doesnt have to be bull strong to keep her neighbors (yours) planter from turning around on her land, just some wires haphazzardly attached can do that. Just something that would scratch up your new john deere planter, tear off some hoses and flatten a tire or two should you want to turn around on her land.  Since you tore out the only barrier that keeps you or your equipment or crop scouts four wheeler off her land without asking, she seems to be rightly alarmed about what her new neighbor is up to.  thats my .02c 

edit: i read your reply that 3/4 of the posts are still there.  i would find some used wooden posts of equal or better quality that what is left standing, replace the 25% you removed and strech three barbed wires.  she should be thrilled.