When you drill the head off the rivet, just drill into it far enough to where the top "donut" of the rivet spins freely on the end of the drill bit. Do not allow the drill bit to continue to drill all the way through the trailer or you will wind up enlarging the rivet hole and your new rivet won't hold too well, if at all. Also, don't forget to apply a small drop of sealant to the hole, (right in the hole,) before inserting and compressing the new rivet, or else you won't get a water-tight seal on your trailer.
"Government doesn't have an answer to the problem, government is the problem." Ronald Reagan