Carolyn Hax: How does a mom explain letting kids live mostly with dad?

— As a Matter of Fact …
As a Matter of Fact …: Funny how we’re all terribly open-minded until we’re not.
I would approach it from that angle.
Actually, I would not get into the details at all and let people mind their own business, unless these potential friendships progress to the point where it’s natural to share. At that point, you can share the details and the funny reactions you get from people. Because that’s more newsworthy than who stays with whom.
Until then, you can say honestly that you share custody, yes? Since “most of the time” doesn’t mean “all of the time” and therefore your kids are with you some of the time. And, scene.
For when you do want or need to share, I would go at it from the open-mindedness angle. E.g.: “The kids stay more with their dad. We’re terribly modern.” Then don’t (over)explain. Plant the idea that if they judge you, they’re being sexist, and let them process it.
For “As a Matter of Fact …”: I can provide some empathy. Your situation was my situation. My son is now 28, but at age 5, a few years after his father and I divorced, he went to live with his father. I had him on most weekends. I was a perfectly good mother, but for reasons that fit all of us, it was the best choice, and I have no regrets.
I did, however, deal with my mother’s confusion and her accusations that I was “giving up my son.” It hurt a lot, and these feelings of guilt and shame carried over into how I felt I needed to respond to people asking me about my child. I did say things like, “We share custody,” or, “He’s with his dad during the week.” But I still felt as if I needed to follow up with “not because I’m a bad mother,” or even the extra-dumb, “Boys need their fathers.”
All of this was ridiculous and not necessary. I did not need to justify our situation to anyone, but I was young, and people are often judgmental.
People also often have rigid views of motherhood and how mothers are supposed to behave and live, and who’s supposed to be the custodial and noncustodial parent.
But I knew my ex-husband and I were doing what was best for our child, and I was grateful that, even though we weren’t married, we had the kind of relationship where we could support our son as we thought best, not as others thought best.
Your situation is not the norm; it won’t always be easy. But you do get better at fielding the questions. Take care of yourself, and don’t ever doubt that you are a good mother.