You mentioned that you could see where the HWC had been stretched or loosened. Was it where it had been attached to the wooden frame?It is, in fact, hardware cloth.
I would second the recommendation above to augment any staples with screws and fender washers, and possibly even then, cover the join with another piece of wood, so that predators can’t work at the bare edge of the wire.
I’m so sorry that you’re going through this.