Blunt question no need to answer on here, does your mother want to take care of him or would she prefer he goes to a care home?
You, your mother and other siblings need to have a family meeting and work out what level of care you can provide to support your mother in looking after your father.
Unless he has a diagnosis of a mental deterioration the confusion is a likely symptom of some underlying condition = he is not medical fit to be discharged. (UTI Stroke etc)
Presuming that your mother is willing to make the changes needed, get your mother to say:
That she is refusing to take him home.
That she is no longer able to look after him safely at home.
That she needs help at home or he needs to be assessed for residential care. This is vital as it will force the discharge team to mobilise all of the services and supports which come with community care.
Then if he is assessed and home care is agreed, no matter what is agreed do not allow your mum to take him home untill all the required provisions are funded and start dates are the day he leaves hospital.
If they need the bed they need to provide step down care.
I known that the idea of a care home (even pre-Covid) sounds horrible but if there is no medical condition it's cheaper to manage an OAP at home.
People don't just fall.
Why it's happening needs to be established is it mechanical (trip etc) or medical (dizzy etc).
At 90 how is his heart, as blood pressure drops due to movement can account for sudden intermittent weakness.
At home has he access to a downstairs bedroom and toilet and wash area
Can the home be accessed without climbing steps
He may likely be recommended a Zimmer frame etc as a tool to minimise the fall risk. These tools need extra space to work.
One of the things the OT will not do is be ruthless in how they currently live.
Your mother (you) needs to look at all the rooms and furniture placements mats etc and ask is it really needed or can it go and if it stays can it be arrange better. This will be as hard on your mother as your father.
If he is refusing your mother's help I would 100% push for a care worker calling in at least once a day.
It would eliminate some of the conflict between them and give your mother some day to day support.
It can be sold as a "help for her" or "as a condition of his release from hospital". You are better positioned to know which approach will work.
In the next few days ask the stupidest, simplest questions. If you think you understand, say whatever is said back in your own words to confirm it.
Get a hardback notebook, which is easy to carry, and a pen. Take notes of discussions and what actions will be needed and who is responsible for the doing.
Best of luck