Coopers Spot-on needs to be repeated after three weeks, as it won't kill any eggs that are on the animals, just larvae/full grown lice.
May be a lot cheaper to load the goats into the back of the car (pygmies?) and take them, BUT it sounds as if mum has a spot of mastitis if she is sore on the side the wee one tries to suckle from. But goats really don't like to be told what to do and how to feed their kids... sheep you can "bully" into accepting their lambs, I would have thought it a lot more difficult with goats.