Can I refuse my mother be sent home from hospital until I have proof she's well?

I hope it's okay to post here. It's not medical advice it's advice on NHS procedure.

I'll try and keep this short but I need to explain the background.

I am a fulltime carer for bedbound mother (75).
For the past few months my mom has been in and out of hospital with the same infection. She seems to get a bit better then becomes ill again and is readmitted.

In October she had a major infection and was in hospital for two weeks (She left on November 1st). When ever she gets a chest infection OR a water infection she is somewhat A-symptomatic and doesn't show signs till she's REALLY ill.
the 4th of November she was back in hospital with an infection again (We believe it was the same infection but can't be sure). They said in the hospital that they didn't know where the infection was coming from but they were confident it was clearing.

They sent her home on the 14th with 3 extra days of antibiotics. by the 20th she was ill again with the same infection. The plan was to send her home yesterday (Friday) but when i went in to visit her on Wednesday she was unresponsive (couldn't wake her up), she was shivering/dithering and wasn't right at all.

I spoke to the doctor who fobbed me off and said "This is normal and is delirium".
She had no temperature, her SATS were all fine etc and she said "You're worrying too much. She's medically fit".
I asked for more bloods to be taken which she reluctantly agreed to. They came back Thursday and her infection markers were up again back to more than they were when she was re-admitted. They changed her antibiotics.

If i hadn't of demanded more bloods she'd have been back in by the end of next week. They're now talking about sending her home Monday.. She seems to be a little bit better but doesn't seem fully right to me. I have spoken to them about more bloods before she comes home to which she said "There isn't any need"..

Do I have any right to say I want her infection markers to be 'normal' before they send her home?