Hi op, I'm sorry you are going through this.
I also strongly suggest going to a recuperation hospital/home if at all possible, toileting is much easier in an adapted set up so if she can recover and get her strength back at a respite home it will make coming home much easier.
Regards the fog, is she drinking enough?dehydration, caused by a fear of an accident/having to trouble someone to help is a major factor in confusion. It is also warm at the moment, I really recommend keeping a running record of how much she is drinking and how often she is going to the toilet.
You also need occupational health to come and assess the house, grab handles in the toilet, on the door, sometimes near the stairs to help with transfer from stair lift to walking. Rollators on each floor so she has something to keep her stable, you can get them with a tray so she can carry things and still steady herself.
For the Bath you can get a electronic bath chair which raises you up and down however still getting in and out can be tricky so she will probably need help.
An electric arm chair can be really helpful, as they help to stand but also can be much easier to sleep in after an injury.
Regards money, there are charities that lend equipment but also look second hand, unfortunately there are a steady stream of second hand mobility equipment at the fraction of the new price.
I'd also recommend an emergency necklace/button so that if she falls etc she can easily contact you. If she won't agree to this google/alexa set to call you in every room.
Lastly you should start thinking about power of attorney, or at least the steps towards this, even getting her to put on her notes that you can talk to the doctor if you are worried can help.
Ultimately if you plan for the worst now it makes the present much easier. I've known lots of people recover completely from breaks and return to their normal lives and I really hope your mum recovers quickly but these conversations are much easier now than when it is too late.