This is an awful situation. Not just because of the stuff itself but because of the karmic lianas that spread througout the whole place taking away every space for breathing. Too much history that prevents new things from emerging.

But as your father is still alive and shares the house with you, he somewhat has the right to have his stuff lie around. The issue is rather that he has no space left (or: enough) to keep the not that urgently needed and important stuff out of your way because the available space is already taken by your mother's stuff. So I suggest the following approach:

As your mother is in her own relationship, there is no lack of money, e.g. € 100-150 / month, to rent extra storage space in the town where she's living right now. There are companies like My Storage that rent out storage spaces as a little as 1 m² on a monthly basis. One can even get discounts for longer perods, e.g., with contracts running over two or more years. (I used that option when I had a water ingress from the flat above mine and had to evacuate my stuff [books primarily] for the flat to dry and be renovated. I paid € 90 per month for 4 m².)

For this storage space there needs to be set up a contract and it needs to be paid for, then there are people needed to help your mother get her stuff out of your house. Obviously she doesn't want to do this because she seems to want to have one foot in the old life and can't let go. (Otherwise she would have done this years ago.) But perhaps repeated urges and telling her this plan may change her mind. And when she finally has moved her stuff, the stuff of your dad can take the space taken earlier by hers.

Hope this helps.