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As the OP said, it’s neither here nor there what you call your own partners and kids, especially if you don’t do it in public. What you’ve heard/read other people calling their partners/kids in public or on social media, and cringed at, is the thing.
In my first office job, late 90s, it was part of my job to check my boss’s emails when he wasn’t in the office. Obviously I didn’t open the ones that were obviously personal, but he had the preview thing enabled that automatically showed you the first few lines of each message. And that was how I discovered that he called his wife ‘Scrumkins’ or ‘Scrums’.
I also used to work with a woman years ago who called her husband ‘Bubba’ or ‘Bubs’ when he came to some after work drinks with us all once. She just called him that all night in front of everyone in a really twee, cutesy way, she said it every single time she spoke to him, which became very grating very quickly.
An old classmate of mine recently paid tribute to her husband on Facebook on their anniversary and finished with “Love you to the moon and back, Care-Bear” to which he replied “Love you too, Bunny-Boo”