Hi Nathan,
In terms of fertilizers, the most you can do is encourage growth of the grass in your hayfield. Increasing nitrogen applications somewhat will help the grasses be competitive against vetch. Also, it would be wise to collect a soil sample and have that analyzed for soil nutrients. If other nutrients are deficiency, those would be worth correcting. That said, fertilizers alone will generally not fully control an unwanted plant like vetch. You might also consider an herbicide.

If you're interested in an herbicide, look into products containing the ingredient dicamba. This is a boardleaf herbicide which will not harm grasses and provides good control on vetch. Some trade names are Banvel or Crossbow. Always be sure to read and carefully follow the label directions whenever you apply herbicides.

Thanks
Gordon