Miss T – I would forget about the cremation issue. That is not going to get you anywhere.
You have already requested the death certificate. That may give the name and address of “the friend” – but unless she is the executor or present at death, it is quite likely the death will have been registered by the Care Home Manager.
Couple more things you can do.
Firstly a search at the Public Guardianship Office to see if sister in law had an attorney or deputy:
Find out if someone has an attorney, deputy or guardian acting for them - GOV.UK (www.gov.uk)
Secondly a search at the Probate Registry to see if probate has already been granted:-
Search probate records for documents and wills (England and Wales) - GOV.UK (www.gov.uk)
You can do an immediate online search there. You can also do what is called a Standing Search (scroll down to the bit about “if the person died within the last 6 months” and do a postal search and you will be notified if probate is granted within the next 6 months.
I think the first thing is to get her name and address and then potentially have a solicitor write to her. If you have real concerns following your initial enquiries, you can issue a caveat (this prevents probate), but that is a step I would not be considering yet and in any event not one I would take without legal advice.