hi watto
sorry, I don't see the problem concerning your brother - surely it's up to your parents whether they are happy for him to continue to live there or not, as long as one or both of them remain in the house - no-one is going to ask him to leave just because your dad moves into a care home (I guess he contributes to the household)
however, if both your parents move out and the money from the property is needed to pay for their care, he has no specific right to remain in the house
in response to your edited post - there may be a problem then, as your brother is not yet 60 - unless he has some disability and is receiving benefits - the LA may grant a discretionary disregard, but that only means that they will come for payment on the death of your parents - there was a recent post in which the circumstances for granting such a disregard were quoted
your brother might buy the house, or rent it at a fair market rate
and just to add, when your dad moves, your mum will be responsible for all household bills (though can take monies from your dad for half the house insurance and maintenance bills)
this is a relevant document - scroll down almost to the end for Property Disregards section 34
https://www.gov.uk/government/publications/care-act-statutory-guidance/care-and-support-statutory-guidance#annexes