Allie, I'm so sorry that your mom continues to deteriorate. It does sound as though she needs to be in a nursing home. If she sends the help away, then there is no sense in trying to set up home care. Over here in the States, Medicaid will pay for a nursing home if there is no other insurance. I don't know what the situation is in Scotland. Will she listen to her partner if he tells her that she needs to go to a NH, but that he and you will visit regularly, etc.? Perhaps he could tell her that it is just until she is better. Having worked for doctors over here, I know that they will usually have a person go to the ER and then do a direct admit to a NH from the ER. You need to have a doctor working with you on this. You cannot be expected to know it all or do it all. Does she have a general physician or family doctor? If so, this would be the one to contact to start with.
It's rather difficult to be specific since you are in another country. Do they have Hospice over there? If you cannot get her into a NH, perhaps you could call Hospice or the Scottish equivalent of that.
Allie, see if you can talk to the doctor about having your mom transferred to a NH once they get her medically stable at the hospital. This would be the best thing for her.