Hi Sophia, and welcome. I'm pretty new around here too. My dad was diagnosed with dementia in February this year and is now in nursing home. I'm in the process of clearing his house out.
Some thoughts about it, based on what I've found so far:
a) Although it involves quite a lot of roaming around the house, I've found that it's easiest to go right through the house throwing out the "obvious" things to throw out first, rather than try to deal with it a room at a time. Stuff sort of divides up into stuff no one would want, stuff someone might want - but not me, and stuff that maybe should be kept. My parents were also hoarders and lived in that house over 30 years
Things like dried up cans of paint, tea pots with broken spouts, bits of wool and material that were hung on to to patch up clothes that are long since gone ...... they're easy to throw.
b) Recycle as much as you can. As with Fair Trade chocolate, there's a lot less guilt attached if it's ideologically sound
Tip: PDSA are often grateful for old towels and bedding - stuff that it's really re-usable but seems a shame to just throw away.
c) Dad has kept all sorts of bit of memorabilia - concert tickets, letters, receipts, etc. I found that heart breaking to think of throwing away ( I tend to hoard similar myself). Instead I've started making him a scrap book sort of thing in a photo album. It gathers stuff together and I think he'll find it interesting and bring back some memories.
As to tips for living together ....... I have none ....... you're a far braver woman than I am