Worried I can't keep mum safe from falls and infections post-chemo

My Mum is having chemo for ovarian cancer. She had her second treatment 8 days ago. In general she seems to be coping well with the treatment.

On Monday (4 days ago) she kept collapsing, going unconscious for 30 seconds/a minute at a time and vomiting. I called an ambulance and she has been in hospital since. 

There seems to be no clear reason for the collapsing and vomiting; no temperature, bloods fine, blood pressure fine and she's had a brain scan which didn't show anything. She's a little better in hospital but still very light headed when she stands and has collapsed a few times while being helped to the toilet 

The Macmillan nurses are great but are really pushing for her to go home as she is reaching the point in her treatment cycle where she will be most vulnerable to infection. I understand this but I think she can only come home if she is safe to do so.  By this I mean she can stand unaided and without feeling light headed. 

I can't be with her 24/7 (and even this wasn't  enough on Monday). I can pop in multiple times a day but I'm not sure this is enough. Really, I think that she needs to stay in hospital until she isn't at risk of collapsing or they find a reason for it which can be managed but by advocating for this I realise that I'm putting her at risk of picking up an infection in hospital. 

I feel there is no right answer but am very concerned she won't be safe at home. She has friends that can pop occasionally in but other than call an ambulance they couldn't help in an emergency ( my Mum is quite large so not easy to get into recovery position, for example) 

Any advice? I feel like a bit of a monster  but I'm just trying to keep her safe.