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Has your wife travelled abroad with your kids and without you?
My kids have a hyphenated combination of both names so with a bit of imagination you can link us to our kids. They have traveled with my in-laws without us without an issue, presumably because we are white and middle class.
If I was in charge of passport issuing for kids I'd add the people who have parental responsibility to the observations section, there are too many family arrangements to go on surname.
(We are aware that our choice of surname for our kids is crap as it is long and doesn't scale if/when they get married or have kids but we couldn't think of anything better at the time and it's not the biggest problem our generation have left for them to sort out so meh. They appear to be globally unique at the moment which isn't great if they don't want to reveal all to a relative stranger, we should all be able to anonymous at times)
My wife and I don't have matching surnames and haven't found it a problem. I'm sometimes called Mr Wife but it doesn't really matter. We haven't had problems at borders and hotels don't usually give a damn!