Paula love, don't give up yet.
Dad is unwell obviously if he needs antibiotics and for someone in his situation coping with the current temperatures must be an added nightmare and enough to make even a healthy person listless.
The hospice nurse will be used to what happens at end of life and they are usually very good at judging these things so think positively.
As for work, what goes round, comes round. Not a naturally vindictive operson I can get very resentful of the kind of thing you are putting up with.
I had in my working life, only the helpful and kindest of colleagues who were there when I needed them so I do feel for you.
All the best, try and keep that chin up like you have all along. Dad is/will always be, proud of you
Take care
Sandra