I think an adult being queried for suitable attire is different to kids tbh. I mean I wouldn't push it and take either of the girls in jeans, but most kids have clothing that's close enough imo.Id really hope that for young kids like yours that would be allowed. But at my club im not sure. The pros im sure would ignore it. But some old duffer i am sure would make a comment and complain.
An adult turning up in leggings or jeggings wouldnt make it onto the first tee. I doubt anyone would actually check the trainers to see if they were golf shoes, but if they looked like trainers its more than possible.
My partner got shouted at for wearing leggings just when walking with me on a nice evening. He did apologise whe i had a word with him.
I dont wear golf clothes or shoes to the range usually. And i didnt have lessons when i started. In fact i sneaked onto golf courses in the evening to learn the game. Which id have no problem with either... id i saw a kid doing this id invite them to join me.
At my current and previous club the old people have been more than welcoming. In fact the owners wife chatted with my daughter last week whilst walking her dog I the course and the club sec got her an ice lolly.