go through U.S. passport control with non-U.S. citizen? [duplicate]

I've done this on several occasions, without the kids. My then-girlfriend and I did not reside together (nor even in the same country). On one occasion, the CBP officer told us we should ignore the airport security staff who told us we had to separate ("they don't know what they're talking about").

If your girlfriend lives with you then you actually must use the same line, because you're supposed to use one customs form for the whole family, and the applicable definition of family includes cohabiting partners:

Effective January 17, 2014, Customs and Border Protection (CBP) broadened the definition of  "members of a family residing in one household" to include long-term same-sex couples and other domestic relationships.

Emphasis added; source: https://help.cbp.gov/app/answers/detail/a_id/441/~/travelers-eligible-to-file-a-joint-or-family-declaration-on-a-cbp-form-6059b

The first thing you should investigate is if she qualifies for Automated Passport Control. You and the kids can use Mobile Passport

Using these services, you (almost) bypass the lines.

Beyond that, the CBP Officers themselves can process any person so any Officer can process your whole group. The question is whether or not they consider you a 'family' since you're not married. Again, it really doesn't matter technically but 'just a girlfriend' and the kids might seem a bit suspicious.

The separate lines are mostly about traffic flow. I think it would be easier to use the appropriate lines but if you really want to stay together, she should go with you and the kids to the Citizen queue.