I will try and keep this as short as possible but it will probably turn into an essay. I have been there, and I've done a lot of finding out since then. As previous posters have said (apologies, I haven't read every post mostly yours) hoarding is an intractable and impossible situation.
Two key things: it's very hard to change hoarders and the professionals are starting to advise that you shouldn't, anyway.
Hoarding is very hard to alter/cure. Years of therapy result in only 20% of hoarders improving, and those are the ones who want to change. The rest are pretty much going to stay that way whatever you do.
But as pp have mentioned above, if a person has 'capacity', i.e. the mental ability to make decisions, then their choices have to be respected. Even if these are unwise. There's a really good blog post on it here by someone whose job it is to decide whether people can be sectioned or not. That post is actually about Diogenes, which is a subset of hoarding, and I'll come back tot hat in a minute.
So increasingly, social services/mental health people are arguing that you shouldn't do a forced clear out or even a total one, but instead work with the hoarder towards 'harm reduction', i.e. making sure they live safely as possible in the way that they have chosen.
Whether Diogenes is a separate thing to hoarding or not is up for discussion, but everything I read about it described my mother to a 't' and it may also describe your MIL too from the sound of it. In which case, you need to proceed very cautiously indeed. These are awkward solitary people - to paraphrase wildly - who would do almost anything rather than lose their independence, including living in a tip. Which means that if they are forcibly removed from their homes, they die far more often than expected. This is what my mother did, when she was in hospital and told she could not come home. (stats: 30% died within two weeks in one study). Google Diogenes, or I can do a longer description of you want.
I went through all of this with my mother and I only wish that I knew at the time that I could not have changed things and perhaps I should not.
So what do you do? Immediately, I would talk, in confidence to the social workers at the hospital. Your DH is right, this isn't a job for cardiac nurses, but they can put you through to the social workers for her ward. Explain the situation and use the words 'unsafe discharge'. Presumably she will need carers but the carers will not be able to come in. Explain this. This will buy you time. I can't stress enough that every single person you talk to will have seen this a million times before and will be as kind and lovely as they possibly can be. Explain, too, that your DH is not facing up to the situation.
You may or may not be able to do this - I have no idea about the distances involved - but if you can get photos, do. Because what will happen next is that your MIL will say that everything is fine, and you need to prove this.
With a week or two bought (hopefully they might discharge her to a convalescent home which saves everyone's face - this was the plan for my mother) you need to decide whether you are going to force her to clear out or just do harm reduction. Social services at the hospital will have contacts for specialist cleaners. They are also always lovely, lovely people and may be able to do a slow, gently clean with her back at home.
But resources for hoarding are almost non-existent. The one set of people who may help (and, because in uniform, your MIL may listen to) are the Fire Brigade. They are v worried about hoarding because it causes fires and makes them more dangerous, and are generally concerned with harm reduction. Could you get them in to advise her how to make the house less hazardous.
Sorry, that's a total brain dump - please do ask about anything and I will explain more.