This works both ways regarding a SC being a visitor. I've seen many threads where the OP gets irritated that DH treats SC like a visitor and does xyz for them...like you would with other visitors.
The narrative changes to suit the argument on the SP forum.
It should be..I'm with my mum or I'm with my dad. Not a visitor in either home.
Visitors (in my experience) do not have a bedroom in someone else's house. He's not visiting.
My DB is divorced. His kids split time between him and his Ex. He goes out when they're there sometimes, just as their mum goes out for several hours at times.
Your later posts say you 'suggested' he takes his DS with him. I'm sure that in the heat of the moment, this didn't come across as a suggestion, but an instruction.
I said in that case please take SS with you as he's here to see you, not me.
This is not a suggestion. It's telling him to take his kid out with him. If you had moved into your DHs house and this happened (still with him having his kid 3 days a week) you wouldn't have said this. It's because you primarily see it as your house
The child could stay in the house and not need to interact with you. How he parents his kid and chooses to communicate him going out for the day is his business. You're not responsible for his child.
At the end of the day, you think you're right and he thinks he's right. I think you shouldn't have said what you did about taking his DS with him, but he could have made his point without bringing your DD into it.
Whether you had a child or not, isn't particularly relevant and it's not the issue IMO. The issue is that that's his DS home 3 days a week.
When tempers rise in an argument, both sides go off the point and the things said at this time become more hurtful than the original argument.