Why exactly do you want to go visit your half-brothers? It doesn't sound like you were ever very close with them, and they didn't make any effort to seek you out before your mother died. The older one, as a bully, will heap more abuse on you. Just because people are related by blood doesn't make them worthy of being called your family; nor does it give them the right to be abusive, physically or emotionally.
You seem to think that the younger brother is a nice enough person. Why don't you invite him to visit you in your city? I can't see why you would want to have anything to do with the older one. Leave well enough alone.