What do you all do with dead animals/skins/offal?

I am probably going to be skirting around some minor legal issues here, but here goes. I am trying to figure out what to do with dead animals and parts that I keep running into. Dead groundhogs, dead raccoon, chicken heads, chicken guts, etc. I used to bury them (which I suspect is partly illegal) but then my dog got into the habit of digging them up and dragging them around the yard. I also tried to put them in a 5 gallon bucket with holes in it so the chickens could eat the maggots. This works ok, even though I still have bones and skin to get rid of, but my wife thinks this it the grossest and most embarrassing thing that she has ever heard of. Reguardless of how much this does or does not make sense, I have decided to forgo this concept for the sake of marital bliss. So, I went back to burying these parts put big rocks on top of the hole to keep my dog out. This works better, but is not entirely satisfatory. I hate going back into the same pile before everything degrades, which means I end up with several little piles of rocks, which is not what I wanted. I doubt a few carcasses are goign to make a big difference, but I also don’t really like burying things in the ground when I drink the water from under it. Again, a few animals aren’t probably goign to matter, but it is turning intot a steady (though small) stream of carcasses and it gives me pause. I thought about dumping the carcasses on the edge of my property where it’s more wooded for wild animals to partake in, but thought better of it because I don’t want to attrack predators. Some I can I get rid of in the household garbage, but the stink and insects it attracts in this heat is astounding. Also, it’s a bit much sometimes. I am looking for more efficient ideas. Any thoughts/techniques to share?