I would agree with Phoenix that trying to reason with your presently irrational wife in a rational way will be an exercise in futility.  I suspect that her issues with the farmer -and with you- on this matter has more to do with perceptions of control and ownership over her surroundings and relationships -ownership and control which she lacks in her own life- than with sheep and grass and tire marks.  I am sorry for you.  This is an awful no-win conversation, and one that will probably morph into the next thing if you actually try to do what she thinks you should.  A rational person might be swayed by discussions of ownership, shared access, and the fact that you do live in a rural area where farmers grass-fed their animals long before your house was built.  I know that I live in an area where if my dog chases the neighbor's heifers, that neighbor has the right (and responsibility) to either shoot my dog or demand that I remove a problem animal from his efforts to make a living, unmolested, on his property.  I have great neighbors but part of our friendly relations are based on mutual understandings of property ownership and respect for both private and shared use.  I would advise you not to discuss your wife's issues with your neighbor; he cannot help her with her problems and you will come off appearing like those strange city people who complain about crowing roosters after they move to farm country. 

Is there anything that your wife values about living beside a beautiful open field populated by sheep?  Anything there that you could work with: neighborly relations, bucolic surroundings, a view to sustainable agriculture, lower property taxes given that she doesn't own the field?

Good luck.