This is how I do it:
Your rivets are either 1/8 or 3/16" diameter. I use a 1/8 drill for 1/8 rivets and 3/16 drill for 3/16 rivets. The head sizes are different, once ya notice the difference, you'll be able to spot em.
Drill gently and stop when the rivet head separates and gets 'stuck' on the drill bit. Ya wanna be careful drilling so as not to 'waller' out the hole if you're going to be using it for a new rivet.
By 'punching' out the remaining rivet, I just use a center punch, ice pick, 3/32" drift, whatever, and push it thru by hand, never pound on it.
Main thing is, ya don't want to count on drilling out the whole rivet, it'll usually spin and waller out the hole, then yur gonna have a hard time getting a new rivet to hold.
Important: For our little trailers be SURE to use 'aluminum' rivets. Stainless Steel rivets are nice but under strain will cause the fiberglass to crack whereas the aluminum rivet will break. It acts like a fuse in an electrical
circuit. Replacing em is easier than repairing cracks.