the parent of one's son- or daughter-in-law, as a common grandparent to one's children
May 19, 2009, Beth Teitell, Horns Come Out When Grandparents Envy Each Other, Most grandparents aren't engaged in a duel with their co-grandparents, but the desire to be the most beloved, most generous grandparent often simmers beneath the surface. ... “It can get to the point where they can't speak to the co-grandparents, or the parents can't have events where they're both there,†she said.
Synonyms
co-parents-in-law (relative to the children rather than to the grandchildren)