I only dabble in trapping, and other than some incidentally snared foxes, I don't trap dogs (way too big of a pain in the ass to deal with scent control). After trapping 50 or so coons though, I have never seen one even attempt to try to chew it's foot/arm off. Maybe it is a regional thing or some other site specific factor is involved.
As far as checking traps, I have never seen a reason to only check them in the morning, unless it is a personal ethics thing. You normally can hide traps effectively if you're trapping in an area where other may see a critter caught. If possible, I usually set them strategically so that I can check them with bios from a distance.
As an aside, as Hank mentioned, coon cuffs are great for coons (skunks get in them too
) but I have caught a feral cat in them as well. Dogs will just dig them up to get the bait, which is nice if you're trapping where yuppies let their dogs run around.
