The 1" x 2" or even 2" x 4" welded wire in a 14 gauge or larger is equal to or heavier than what most live traps are made of, so it should be sufficient to repel all boarders. Unfortunately you found out the hard way that chicken wire / poultry wire is good for keeping chickens in but won't keep predators out. A determined varmint will blast right through it.
The apron should run up on the sides and extend out from the bottom at least 18 inches and 2 feet is better. Again the idea is they will probe the along the base of the wire, but never do figure out to back out from the fence and start their tunnel back there and go under the apron. They are smart, but apparently not that smart.
One might be tempted to use zip ties to secure the wire apron under the gate, but I'd use wire instead. Maybe wrap it double and space them about 6 inches or so. That is where they will come back to to test it. You don't want it to fail again. And make sure the gate is secure, with latches that can be locked / blocked to prevent them from flipping them up. A little piece of wire or similar is all it will take.
Hate to see you get started like this.