You found yourself having to take on two kids, one of whom you didn't like much for a start. It was never going to be easy, but I think the issue is that you've decided to not trust your OH when really, if there's a time to do so it's now. I expect that's what is making him angry towards you.
You seem to have totally missed the point about the day out to the museum. Your OH wanted to encourage all of you spending time together. You do to pick and you picked an activity that most 10yo would have hated. Why would you pick this in the first place is odd. There is therefore a good chance that your ss could have deducted that you did so on purpose. Not the case I'm sure, but the mind of a 10yo would have easily believed it.
He goes, he's not happy (of course not!), but he goes. That means that he made a real effort for the family. Sadly, your OH shouldn't have had to ask you to say thank you, it really needed to come from you. You should have got home, told your ss that you understood this wasn't his favourite activity, but you appreciated that he made an effort to please his dad and that he showed how mature he was. Instead, you took the attitude that it was normal that he should be forced to do something he disliked to make you happy.
It's no surprise things are not working out and your OH is frustrated with you. I would be too if I were him. His priority right now is his kids who've been emotionally hit badly by their mum abandoning them. He wants to show to them that the problem is with her, not them, that they are loveable and that she hasn't left them because they were not good enough for her. Yet here you are unwilling to consider what you can do to help them emotionally to feel better.
It's not your role to make them feel good about themselves, of course it isn't, but your OH is asking for your help right now, and instead of doing so, you are battling against him because you are not happy is giving you less attention at this time. Sadly, it's a vicious circle because the more he is left to feel guilty about trying to be a good dad and making up for their mum's failure, the more he has to cope with you asking for attention, the more he is going to feel that you only want him for when everything is good but not prepared to be there for him when things are tough.
I think counselling is indeed the way to do, but try to listen to your OH and trust that he is doing his best in a very difficult time. He can't mess it up. If he isn't there for his kids now, the emotional damage could be permanent. So no, it's not about him being a Disney dad, it's about him trying to help his kids move on from the damage their mum has done.