This is a bit of a tough one, I’m going ESH (except the kids).

Yes, your Husbands child is not yours, and you don’t owe anything to that. That doesn’t make you TA. You have fostered an environment for your son and his half-brother. You’ve allowed the half-brother to come to your house. There is nothing wrong with that (actually, it’s commendable). For the children involved, it may be confusing on what’s ok, or not. So I can see how this confusion happened between kids.

Where I do find you a bit of TA.

I have a child from my first marriage, relationship ended badly (similar to yours), as my ex wife was cheating. So, I’m speaking from experience. I still have to keep a respectful relationship with her. This involves talking about trips, vacations, visitation, healthcare, the works. Why didn’t you tell your ex husband you were taking a trip? It involves flights and hotels, so I’m assuming you are crossing State Lines.

A simple conversation would have avoided this whole situation. “Hey ex husband, I’m taking bio-child to Disney, this is the days we will be gone.” If ex husband said, “what about half-brother?” You’d be able to respond with “if you want him to go, you will have to pay for half-brothers trip”. Or “I would prefer to take bio-kid alone.” That simple conversation would have saved everyone some heart ache and hurt feelings.

If you did have that conversation, I would push you to NTA. But how in the dark your ex was, and how the kids thought it was ok, I’m assuming the conversation didn’t happen. Communication with an Ex can be difficult, I don’t argue that. But healthy conversation is vitally important. Good luck.