Hello, I am Dr Helen, a UK doctor and GP.
Your mother-in-law is right in what she says. It is not possible to have a home consultation for anything in the UK with the one exception of terminal care where dying patients are visited at home. Likewise physiatristy is not a recognised speciality in the UK. It is still very much a US speciality. We do have rehabilitation medicine which is probably the closest but is reserved for stroke and injury patients on the whole. UK dementia patients are looked after by the psycho-geriatricians and the GP would do the referral to such a specialist. The general geriatricians would be the best speciality to review his pain and mobility problems.
The UK health system is, as you say, very different to the US. I am UK born and bred but have US doctors in my family and know that the differences are quite astounding! The GP is the gatekeeper for everything here. A person can ask to see a specialist privately, rather than on the NHS, but still has to see the GP first for the referral. You cannot self-refer to a specialist.
A lot of US expressions don't even make sense here....the phrase "certified" for example means you have been detained under the mental health act so for UK patients to see a doctor describing themselves as "certified" can be quite alarming!
I am sure the GP could arrange further referral for your father-in-law and GPs are very reluctant to throw people off their books. That is reserved for aggressive and violent patients who continue to threaten the GP/clinic staff so you can reassure your mother-in-law on this account.
I hope this helps. I'm happy to help with any other questions you have.
I joined JustAnswer in June 2013 and am a UK doctor. I have been qualified for 23 years and have widespread experience in GP and cancer care.