“Intentional families” is a phrase I don’t use. It is sometimes used to refer to families where a child is adopted or born after a gay or lesbian couple is together. This is to distinguish such families from the ones where the children are from a heterosexual marriage and the parents divorce because one comes out as gay or lesbian.
While “intentional” is empowering to such families — as in yes, we are a family and we want it this way — by default it implies that the other kind of family is unintentional. This was first pointed out to me by a 13-year-old girl from a divorced family with a gay dad who asked me, “If they’re intentional, then what am I?” So out of respect for the many ways that kids of LGBT parents come into our families, I differentiate the two experiences by saying “children of divorce”, and “children of gay union.”