That sucks. I haven't had any trouble with my IceFalcon mail & pliers. I'm surprised the GDFB pliers just broke so quickly and easily. I have the IceFalcon and Historic Enterprises pliers, they both seem sturdy.
Regular pliers would work fine, the key is to make sure that the hole for the rivet head to sit in is the same diameter and depth as the head, or it will not rivet tightly and/or may bend. I think the type of pliers you'd want to look for are "bull nose" pliers, they are shaped more like the mail pliers (wide and short) than standard pliers (thin and long).
Post pics of how it's unset and unaligned? It might be easily fixed.