I think YABU overall.
If your children are teens they are surely used to doing things with just their parent, they won't view the partner as their parent and may prefer being with just their parent. Even if they don't, it should at least be "the norm" to them.
I have to say, if I'd had a raging row with my DP that included threats of breaking up, the absolute last thing on the planet I would want to do is take my DSS out without DP, to see my family. The best place for him in that context was with you. Your DP would have been resentful and possibly prickly with him, and your DS would have just witnessed him falling out with his mum, aware of the tension, and probably feeling pretty awkward. They're not oblivious little kids, they're too old for you to just pretend it isn't happening. Your DP obviously doesn't view your son as his kid, and it's very unlikely your DS views him as his dad. Why try and force it?
And lastly, how special can two teenagers view the coronation as, that watching at home with their mum wouldn't satisfy? I know there was talk of street parties but I don't actually know anyone that's done more than just watch at home, especially of that demographic.
Having said that, it would be interesting to know what the row was about, as that could change minds on who was reasonable and who wasn't.