Re read my post, think about and then let me know what your thoughts are.

Specifically the part, "if the opposing land owner wanted to put up new fence we would probably be open to working with him".

If he doesn't want to put up the new fence for his livestock we are just fine with the current fence.  We currently do not have any livestock grazing on any land, all of our hogs are in hog buildings.

No one other than my family has spent a dime on fence to contain livestock that belongs to my family.   (Edited to add ---->)  We haven't requested anyone else to spend a dime containing our livestock either.