I think at the moment, the hospital has duty of care for her. Whether she's self-funding or not, they can't just discharge her into a vacuum. There has to be some liaison. So, yes, you are entitled to see the hospital SW. (But willing to be corrected, if wrong. It may vary between PCT's.)
Ime, everyone has their own agenda. The hospital will want her bed when they've done all they can do for her medically. The SW will probably be wanting to see you to find out where they can discharge her to!
In our case, the LA was involved because my mother had been in her own home with visiting carers, partly funded by them. But because she owned her own home, she/we would have to sell it so she would be self-funded in residential care. (The doctors said she could not return home.) The LA would pay for the first month, I think.
So they then had a battle with the PCT over CC. Neither wanted to pay for her. Both sent assessors to the hospital and we were informed so we could be there.
She was given a date for discharge, practically as soon as she arrived. When she was put on the LCP, my agenda was that I didn't want her to be moved. I asked how close to death they would move her and they said Cheyne-Stokes breathing - which I thought was appalling. I knew she was dying and wanted to be at her bedside, not looking for residential care.
She would have been discharged to an emergency bed in a nursing home in her LA, which wasn't even in the same county as the hospital.
Fortunately she died before this could be arranged.
In your case, it sounds as if it could be more long-term and my mother didn't have any behavioural issues. But the protocol might be similar in your hospital.