I hope you understand that by doing so, you placed your interviewers in a very awkward position. It would be the same if you revealed to them your e.g. religion or sexual orientation, when they never asked. It smells like you were setting them up for a future lawsuit.
The reason every startup asks "so what do you like to do for fun" in interviews is that kind of "cultural" fishing. The OP is just flipping the game around.
The problem here is that familial status is legally protected, so by bringing it up it puts the interviewer in a tight spot. If I reject a candidate who states such things, then there may be lawsuit risk, and my superiors may not be sympathetic to the fact that I did not ask the candidate.
Unfortunately, I don't think theres a way out of this problem. Family friendliness is probably the most important culture question for anyone with a family. The only solution I can think of is to dig up information online from previous employees, but that is a crap-shoot for small companies.
More accurately, a company is not generally allowed to discriminate in hiring on those basis, and thus will generally have policy in place not to ask about those things. The law doesn't actually prohibit asking, it prohibits discrimination on those bases; but asking the question is something that can be used as evidence of intent to discriminate.
Of course, someone volunteering the information is substantially different than the company asking it.