What kind of goats are they? If they are standard dairy does, 2 months was too old to try to disbud. Did you see the kids before they were disbudded? How big were the horns then? If the nubs are 1" tall now they are definitely growing horns. I disbudded my dairy kids at 1-3 weeks depending on breed and sex.
You can try disbudding paste. Some cattle people use it. It is very caustic, so separate the kids from each other so they don't get it in their mouths, etc. Don't let your children play with the kids while the paste is doing its job. I don't know if it will work, but if you don't want to dehorn by a vet, it is worth a try. I would check it out on line first.