To put into perspective how seriously this mistaken is taken by the industry, sites and models in particular, a bit of OG context:
Years ago, a model on Streamate was actively advertising her toddler for sexual activity. This was caught not by site support, but my fellow models who, for the sake of the child who was being horrifically abused and the basics of common decency, documented and reported everything not just to the site, but to the authorities. We're talking FBI, police, everything. And Streamate did exactly the same, turning over all relevant information on the performer to the authorities and instantly banning this woman within an inch of existence. The child was pulled by protective services, thank fuck, and the mother arrested and charged. But none of that can erase my memory of comments made by the members who were in that room, egging this "mother" on, sexualizing this poor child, and being vile beyond the telling of it.
Not just because it was the right thing to do, but because that was the minimum reporting requirement for something like this least they be held legally liable.
There's a lot to unpack there, but the gist is this -- while what you're describing certainly doesn't rise to the level of the above piece of human garbage, it still exposed your child to people who actively had a hand on their genitals. Sit on that for a minute from an outside perspective. Best case scenario, no one did anything besides report it and GTFO. Worst case, someone did -- screenshots, recordings, and worse, to use for even-god-doesn't-want-to-know-what in the future.
Accident or not, fluke of technology or not, that level of mistake is the sort of epic fuck up that no site can risk. Even if you somehow did get your account back, and god knows I'd never want to touch anything to do with it again, the best case scenario is that some asshole shows up every so often to remind you of that time your kid was on your stream and makes a vile comment about it. This isn't a one time incident that goes away; the internet remembers.
Also, and by all means I am trying to freak you out a bit here, should anyone have personally identified you, it would've been grounds for child protective services to investigate your fitness as a mother and potentially take your child. Models have lost custody for camming in the same home as their children. CB could still report you, and may be required to by law. Like, that bad.
If I were you, I'd be nuking that entire persona before even considering a new site with some serious parental controls in place. At minimum. Because you're not getting that account back and, frankly, you shouldn't want to. Personally, I'd be taking a long, hard break from the online adult entertainment industry.