Is the questioner considered negligent in the care of his deceased brother, who was ill and suffered from a severe disability, for not taking him out of the house or sitting with him for sufficient periods, despite providing him with comprehensive care and meeting his basic needs?

There is no blame upon you for what you mentioned regarding leaving your disabled brother, for it is not religiously obligatory for you to take him out for a stroll, especially given your excuse that he cannot control himself, and that this matter did not cross your mind. We hope that Allah will reward you for what you have done for him, so cast away your regret and sorrow, and do not repeat "if only I had done such and such," for it opens the door to the work of Satan. Seek Allah's forgiveness for your brother and turn to acts of obedience.