I have Parkinsons as well, @BigLittleRedOne, and I am in my late 60s. I live in the UK - and have always done so, so unfortunately I can't be of much use in regards to helping you with the logistics concerning your DM returning to the UK.
However, I do know a reasonable amount about having Parkinsons, as I was diagnosed with it quite a few years ago. It might be helpful to know where you live OP, as at first I thought you lived abroad, in the same country as your DM, but you have at least twice mentioned the UK as being 'here', not 'there', so I am slightly confused about what is confusing you. If you do live here, do you know why your DM wants to come back here to be near to her siblings, but not to you?
Anyway, you may already know about the type of Dementia most commonly found in people with Parkinsons, which is Lewy Body Dementia. If you are not already aware of it, you might be able to see whether it seems to match your DM's symptoms quite closely or not. However, even if it does seem to show that your DM does have that Dementia, it still isn't necessarily the case, as the symptoms you describe are ones that I also have, and I am reasonably sure that I have not - yet - aquired any sort of Dementia.
The most upsetting of the symptoms that you have told us your poor Mum suffers from, is to me the lessening of my emotional range - my whole personality has always been based on how much empathy and care I have always had for others. To be able to recognise in myself that I am no longer feeling such a strong range of emotions, is very strange indeed, and to a certain extent I wonder if that actually happens to most people who are just ageing, in order to help us protect ourselves against all that we lose the older we get?
Apart from natural ageing, the majority of the symptoms you say your DM seems to be experiencing, are actually part and parcel of both Parkinsons, and often the medication we take for it too. I have been taking Co-careldopa for quite a few years now, and I can't distinguish between my tablets and my actual condition.
Good luck, and best wishes, in getting the most appropriate, and best care, for your DM @BigLittleRedOne.