If my X has now moved her grandfather into the home she shares with my daughter is that considered cohabitation. I know it is not a sexual relationship, but he is of the opposite sex. Is this grounds to stop paying alimony?
No. Per NCGS 50-16.9(b), cohabitation means the act of two adults dwelling together continuously and habitually in a private heterosexual relationship, even if this relationship is not solemnized by marriage, or a private homosexual relationship. Cohabitation is evidenced by the voluntary mutual assumption of those marital rights, duties, and obligations which are usually manifested by married people, and which include, but are not necessarily dependent on, sexual relations.
It may be a reason to seek a modification though. If he is providing support/income to the household, this could arguably be a substantial change in circumstances warranting a modification. In my opinion, it may be worth seeking a full consultation with an attorney to discuss your options.