> There are women who find the joke funny and who don't think it's sexist, and FWIW my wife is one of them.
Women can be misogynist. What is your point? We live in a culture still filled with everyday misogyny and sexism (and racism and other forms of bigotry). Misogyny or sexism isn't some innate character trait like a gene deficiency or something you get from exposure to gamma rays. It's something you do and behavior is specifically influenced by the culture around you.
There are still comedians "the ol' ball and chain" routines and how they hate their wife, basically, and there are still women and men who laugh at it (usually for different reasons).
There's a well-known phenomenon where women in positions of power will actively sabotage women under their authority and "kick the ladder down", often to avoid risking their position by being seen as "another woman" rather than "not like the other women". Even the "girl boss" trope liberals seem to enjoy so much is usually based on superficiality and suppressing womanhood. It's very much about "carving out a space" for some women who do the part and try to fit in with the men without challenging the need to fit in with the men in the first place.
I'm not sure what you're trying to prove by citing more reasons to dislike VdL when I literally already told you I strongly dislike her. My disdain for her goes all the way back to when she was the figurehead for Internet censorship (i.e. DNS and IP blacklisting) and tried to justify the extension to government power with "fighting CSAM" and implying anyone opposing her project was a pedophile.
When your joke only works because she is a woman and mother, it's extremely likely that your joke is sexist or misogynist because it relies on sexist or misogynist subtext to work. "She has more children than working fighter jets" only works because she is a woman and a mother. You could make that joke about a man but it would have very different subtext, i.e. a man having a lot of children implies being an irresponsible womanizer: you could have made that joke about Berlusconi for example to build on his reputation for promiscuity and irresponsibility. It would be a very different joke.
> Does she have a value system?
Yes. She's a "liberal conservative". I realize this sounds nonsensical in the more widely used American sense of those words but it's a thing. I think the US equivalent would be something akin to neocons, expanding state authority while simultaneously reducing social services and deregulating markets. She luckily hasn't been very successful or coherent in practice, though.