If you tell hospital, and preferably documenting everything, then they know that sending her to her home will be an unsafe discharge.
I was surprised to hear of stepdown hospitals being closed as they've been the cheap answer for some time to bed-blocking, but each authority makes different choices to stay afloat.. It's worth seeing what exists in your health authority area. They are sometimes refered to as rehab units when actually being stepdown with rehab.
She is highly likely to be entitled to six weeks of re-enablement care at home, if enough space can be made.
You talk about going and clearing your mum's home, which is why she's not letting you do anything. It's her worst nightmare; being forcibly cleared and not there to make any choices, or have discretion and her dignity be maintained in her neighborhood.
If she's coming towards the end of her time she may well want to just go out peacefully with things as they are.
Assuming the home is just hoarded with too much stuff, (rather than a collapsing squalor hoard) then what she needs right now, is enough moved from one room, corridors to bathroom, and bathroom, and a microwave, and it's possible for carers to attend. (Quite a frequent solution in hoarding and carers)
If you approach her with moving stuff, not chucking stuff, you have a better chance of co-operation, though it doesn't sound like there's a happy relationship to try and build on.
You are entitled to lay out what you can and will do, and what you cant and wont, and hold those boundaries, and she is entitled to have her boundaries including around the visual results of her MH condition and accept the lesser of bad consequences as she rates them.
Hoarding is the visible symptom of a complex MH condition, it doesn't make the person lack capacity. We are entitled to make poor decisions, unsafe decisions, and decisions that make little sense to others as long as we have capacity..