How much does family mean to this prospective man or woman? Will you become their light and their world? Will you turn into each other's nuclear family and relegate immediate family members to the "extended family" bracket? Will your children strengthen the bond you share or weaken it? Will the new "extended family" prioritize the health of *your nuclear family unit* (good!), or you and your person as individuals (bad)? These are questions you need answered—never verbally—but by the actions of your prospective person in the early stages of the relationship.
However, contrary to the previous entry, the relationship between your person's parents and their own parents is irrelevant. Take my ex's mother as an example. If you had attempted to predict the answers to the aforementioned questions based on her parents' history, you would have been dead wrong. Both her parents are (or were, at the time of writing) borderline estranged from their respective families, spending the bare minimum amount of time with them, and yet, had I applied these heuristics early on in the relationship I would have ended it right then and there. I was the stranger. Never the priority. Always in the line of fire and unwarranted subterfuge.
This wisdom becomes crucial when dealing with self-improvers recovering from wounds inflicted on us by our parents, since close proximity tends to trigger regressions and may inject turmoil into the relationship.
Have your children's back, but later, their family's back (once you are relegated to the extended family bracket). At times it might seem like you're putting their family above even themselves, because commonly what's best for their nuclear family unit is ultimately what's best for them. Never undermine their significant other, never* fight to dissolve their family unit.
* exceptions being cheating and unwarranted use of force