My yard is full of this vetch, which to me, though it has lovely flowers and fluffy leaves, is an invasive weed because there’s no containing it. I learned that one of my neighbors gave another neighbor a lovely hanging basket of it a few years ago!! Gee, thanks.
Try the Ormamental and turf herbicide Lontrel for your vetch problems in bedding areas. Read the label carefully. http://www.cdms.net/LDat/ld2QB003.pdf
It is not labeled for use in Residential lawns but it can be used as a spot treatment in residential bedding areas.
It is very effective at cleaning up vetch in junipers.