That's quite a conundrum.
I think your only option is to put the lid on and leave it. Maybe in 10 years it will have broken down into something you can deal with
Buy a new bin and start using that.
Its not the actual bin we use, its an old metal one a friend used to use to incinerate stuff in my back garden.
Its just sat there being disgusting haha.
Find a handy letter box (Standard GD reply)
How long have you hadthe dogs and how long has your wife been doing this?
We have three medium dogs and they'd ¾-fill a dustbin in just a few months. Given that you have large dogs and there's a whole garden out there, where's the rest of the poo?
Also bear in mind that, since you seemingly don't clear it up very regularly, the dogs will likely have walked that **** all over your house...
There is your answer. Burn it!
Does anyone want photos? hahaha
How do you set fire to 3/4 of a bin full of flooded out dog turd? Can't imagine it's very combustible.