Yes 7 year rule re social care purposes, the cap is £23,250 (under care is free, over is taking into account for care costs) the legal term for offloading the house or any other part of a persons estate is 'Deprivation of Assets' If the Local Council decides that assets were moved etc to avoid paying care home fees then these assets will be takin in as consideration as if they still owned them.
Suprised not one has mentioned a 'Deed of Trust' instead of giving it over or selling, you get a Solicitior to draw up a Deed of Trust this can show all beneficaries (op mentioned three) on it Can be held at Land Registry or with Solicitor, basically the deed shows the house is actually owned by the persons named on trust and your parent/s live there until the day they pass. This will still be looked at as above though.
Link here for age UK explains prob all you need to know
https://www.ageuk.org.uk/information-advice/care/paying-for-care/paying-for-a-care-home/deprivation-of-assets/