That does sound a quick progression. My mum was much slower but a stroke & heart disease intervened. If your mum is social care funded I'm surprised they haven't asked about CHC. This is Continuing Healthcare funding, so means the bill gets passed to health. I don't know whether this would make a difference to your current concerns but it might do if the home is putting in a level of support that is beyond what they're actually resourced to do. This is often the case when people challenge, sadly.
Sounds like you've been dealing with a lot if she was at home with you. My Dad looked 20 years older after my mum was sectioned. I've found the support group website. I've forgotten how to link on the iPad but you can copy & paste into your browser:
www.ftdsg.org/Regional_contacts/
my mum used to ask to go home, or tell me she was going. I used to just reflect it back to her " you want to go home", and didn't get into a debate about why she couldn't. She was very aware of where she was so you couldn't go along with it like you might for someone with Alzheimer's (where you say "ok, let's go", then get your coats, go for a walk and then come back for a cup of tea - you might be able to do this once her short term memory is shot).
It is very tough, but if this is any comfort my mum died last April, and since then the memories of her with FTD have faded and I think about her much more as she really was. It is hard to remember the real person when they're in the grip of this.
One other thing is that I did a photo life story book for my mum when she was in care, partly for her orientation, and to use as a talking point with staff, but also for me to help me hold on to who she really was.
Best of luck with everything. I'll check back here again in the next day or so.