AITA for telling a woman off after she asked me to put on clothes at a nude hot spring?

I'm using a throwaway because I'm not gonna become known as the nude hot spring guy

So, there's a natural hot spring only about an hour drive away from where I live. It's on public land and a relatively well known hot spot (get it). The hot spring explicitly allow for nudity; and there are signs up warning prudes who have complained for years that, yes, people are allowed to be nude there.

I've been going there about once a week recently, and every time I get nude. I like to go Sunday mornings because it's mostly empty. Last Sunday, I arrived and stripped down as normal. There was another woman there who was using the springs as well and I chatted with her a bit. After about 20 minutes another woman arrived and came over to talk to me.

This woman explained her 3 kids we're around the corner and wanted to the use the hot springs. I could see them down the trail, they looked to be in the age ranges of 12-6. I was really confused because there was plenty of room still so I told her very confused "ok?" She was trying to "subtly" tell me what she really wanted, but had to spell it out for me. She then asked me to "get decent." I was just taken aback at first and told her no, I wasn't done using the spring yet and I only had the clothes I was going to wear back home. She then told, not asked, me to leave so her kids could use the spring.

This pissed me off so I told her to go fuck herself and we argued for a bit. She ended up storming off. The lady who was in the spring got out and told me I'm an asshole, so I called her a bitch.

I left about 20 minutes later and saw that the woman and her kids walked back to their car. I waved at her and said to enjoy the hot springs and she flipped me off.

While I was really angry in the moment, I'm starting to feel like I got dragged down to her level and made an ass out of myself. Opinions?