Is it permissible to treat and honor disbelieving parents, as well as disobedient relatives and kin, in a manner that outwardly appears affectionate without harboring such affection inwardly?

Kindness to a disbeliever and showing him benevolence is permissible. A relative is more entitled to benevolent treatment, especially parents, for being kind to them is obligatory. As for affection, its ruling varies depending on the types of people. There is no harm in showing them affection by way of outward amiability, while detesting their disbelief and transgression.