Just to be clear, your mother has a house in the UK where she's hoarding things, the house has now been deemed a hazard as a result of that, so she's currently living with you? She is presumably of Cypriot heritage (or previously lived there) and has a bank account in Cyprus? She's traveling to Cyprus regularly and this is when you allege she has been taken advantage of and has withdrawn the money?
How often does she travel? It would be virtually impossible for one person to bring 100k in cash into the UK in one trip undeclared. It would be possible however for them to bring it in in installments if they travel regularly. I sincerely doubt someone with suspected dementia would be able to navigate this long term though.
But are you absolutely certain (and if so, how?) that your mother has not taken the money back to the UK?
You say she's a hoarder and has issues - is it possible that she's hidden the money in her UK house and forgotten about it? Or disposed of it some other way?
You say you have no 'proof' that she gave it to these 'friends', but there must be something compelling you to suspect them of taking it.
I understand that dealing with police/authorities over there is quite difficult (I briefly worked with a company based there and heard some horror stories) but unfortunately that is all you can do in terms of recovery.
The most important thing to focus on now is that you MUST get power of attorney and take control of her finances etc immediately. If she's at risk you'll be able to stop her from traveling and handing any more money over at least.
If she does indeed have dementia, she could well be incapable of understanding the implications of what she's done, so don't hold it against her. She may be confused, embarrassed, or oblivious; either way, you may never be able to get her to understand/accept the gravity of what has happened.
IMO your priority now should be protecting her from further harm. Pursuing the lost money (assuming it has actually been given to these 'friends') should be next, assuming you have the bandwidth.