Unless you omitted details this simply isn't true, is easily found on the US immigration site (as referenced already). So I'm not entirely certain why a google at the counter couldn't yield this information for you, took me 90 seconds to confirm. The counter worker for an airline has no business or benefit doing this when they're clearly wrong and a higher level of authority needed to be included.
Fwiw, when I originally applied for a visa I entered my name First Last and it was rejected because on my passport is First Middle Last though nothing on the application stated ‘as it appears in your passport’. I had to pay and apply again.
My point, don’t leave any room for something to go wrong, you could very well be sent back at the border. 🙏
I’m a diver so Samui is obvious for me but Chiang Mai is a bit less expensive overall. But as mentioned the smoke gets pretty bad in the north because it’s also coming from Myanmar and Laos.
Fwiw I’m in Khon Kaen and one thing I see a lot of is families and children.
Warning, keep your dog close and confined. Soi dogs run in packs and can be dangerous.