Won't comment on the poly stuff, since my own life is on the rocks when it comes to that and I don't trust my ability to say anything constructive on relationships anymore.
But my mum also has cancer, she didn't undergo chemo though but is generally in a really bad shape due to a mass of existing conditions to top off her incurable cancer thingie. So I really know (or think I do) what you might be going through, and am PMable if you want to talk.
As to the boy - I don't know what the German system is like but are there any family services available via school or the social services in your location that could start addressing the home situation in a respectful, non-intrusive way?
I know beer is a HUGE part of German socializing, but isn't your country famous for various non-alcoholic beverages that look, smell and taste like the real thing?
Me: bi female in my twenties