FWIW I would split it into thirds.
I earned the same as my ex. He had 1DC and when discussing living together we agreed to split things according to "fiscal parts". Where I am, an adult in full-time employment is 1 whole part, and a child in their custody is 0.5.
I was 1 whole part or 40% of the 2.5 total, and he and his DC were 1.5 parts or 60% of the total.
I think your problem is that your DP is not allowing for the fact that he has chosen to date a person with children. I could have argued with my ex that I'd pay only 1/3, but that would have completely ignored the financial reality of dating a parent.
He is entitled to his opiniona nd money is tricky, but given his reluctance to participate financially in a kid-focused get away, I'd leave him out of this holiday.
I'd have a calm chat later about how he sees things if/when you do have kid-focused days out or trips, or if you eventually end up living together. If his attitude is entirely "your DC are your own and I am not prepared to subsidise them", perhaps he is not step-dad material.