This is a difficult one, partly because you have no status as your friend's spokesperson or representative, and (I assume) no-one has power of attorney.
What she could do, in the presence of staff, to try and make sure you are not manipulating her, is to state clearly that she would like you to be involved in her care planning; and then ask the staff to make a note of this on her medical records. This has no legal status whatsoever of course, but it would mean that she had stated her wishes, and ward staff are usually fine to have a friend by the side of someone with no living relatives. It is a grey area as, in my experience, there are sadly "friends" with vested interests of one sort or another - I am not suggesting that you fall into that category, but just trying to explain the situation.
Sadly it is very common indeed for an elderly person who has been managing reasonably at home to start to deteriorate after and fall and/or a hospital admission. This happens all the time, and it is not always because of the hospital's treatment of them, but simply because the fall is indicative of a process of deterioration, and precipitates a worsening decline.
Of course being in hospital is far from ideal, as the staff are often overworked and some of her care needs might be met in a different way from at home - e.g. the use of pads or a catheter. And hospital is of its very nature a bit of a dangerous place for the frail elderly - there are long walks to the toilet, higher beds, strange environment, slippy floors etc.
Physiotherapy and encouragement to mobilise is there, but only once a day for a brief time if you are lucky. In between those sessions, the staff simply need to keep her as safe as they can.
And it is very common indeed for an elderly person who has suffered the trauma of a fall to become a bit muddled - even if only by the surroundings, which are unfamiliar. When you, a known and loved person, roll up they are likely to seem entirely with it; but in the depths of the night, or after just waking and not finding themselves at home it is likely that they might be less on the ball.
So - being in hospital is not ideal for this lady, nor any elderly person, and the staff know that. I am not making excuses for the system, but just stating that this is how it is, and this is the effect it often has on older people. If you feel there are strong grounds for complaint, then PALS is the route to go down, but it is very possible that the staff will simply state that they are following protocols for her safety.
I do know how frustrating it is to be sucked into these systems and to feel a bit powerless - I have been through all this with my OH, and there is no doubt that the system has its flaws.
If you are saying that she needs to be at home, then you need to be talking to them about what you have been doing for her and what, if anything, you might be happy to do for her in the future at home. Before she leaves to go to any destination (her own home or wherever), there needs to be a care plan put in place for her, and you could ask to be involved in those meetings as a concerned friend who is prepared to part of her support system at home. However, I would caution you that, however much you love her, it is a distinct possibility that she will be less able when she returns home and not to take on too much. The statutory services should be the "go to" option and you should be additional to that. You could find yourself with a huge task on your hands.
But I would concentrate on getting her moved to her next destination rather than dealing with complaints which will "do your head in" for sure.
I wish you lots of luck with this.