Is informing the family about the deceased husband's relationship with another woman — given that he was known for his righteousness — considered an exposure of his affairs or a harm to him in his grave?

Your mention of your husband's relationship with a foreign woman after his death, in front of your brothers, is a forbidden scandal, a breach of what was commanded to be concealed, and a prohibited backbiting. If what was reported is not true, then it is a great slander. Both are major sins. Your grief and curiosity are not justifications for backbiting. Seek forgiveness for your husband and repent to Allah for backbiting about him, and conceal his faults; for Allah loves concealment.