Oh dear...you're one of those parents, aren't you OP.
I have 'my spot' on the sofa. The DDs don't tend to sit in it, and if they go so far as to sit in it, they are asked to move pretty sharpish.
As for being 'equal' hmmmm, well in some ways, yes. But I would describe our relationship in terms of my being the benign despot and the DDs my cherished minions, living under a caring dictatorship...
OP you say your nephew is having a very stressful, challenging time at the moment, and was staying with you for a bit of peace & quiet, I take it?
Then why on Earth did you take a complete non-event, and escalate it into a needlessly uncomfortable situation and create an awkward atmosphere for your nephew?
I bet your poor nephew went to bed feeling anxious and stressed, and very much aware of a bad atmosphere.
Well done.
To be honest OP you say your DP is childish, but you don't sound any more adult.
I, on the otherhand am a proper grown up with a huge bag of common sense to hand. If (and it's a huge if) you felt your DP's attitude was unwarranted, then the sensible thing to do, was have a quiet word with him about it when your nephew was out of earshot.
Instead, you took a very, very, very slightly awkward blip, and turned it into a fullblown drama...casting yourself as the noble heroine championing children's rights.