I had the same thing with my mum , a bit worse than your photo. She will hate it if you do it and probably accuse you of wanting her stuff for yourself. If she is willing , get some one in. There are people who do this better than we can and she won't hate you if she agrees. If she doesn't agree to the clean up , just leave it and visit her in parks or cafés and have a laugh instead of seeing all the stress mess. It won't stop her hoarding unless she goes to counselling