You can't have an "equal" say in this situation so I think the final say should be the parent not the stepparent, particularly as he is expected to pay for her children to go on holiday with them.
This is absurd. "he" is expected to pay? The OP doesn't say who earns the incomes in their home - it may be that she is the main earner, or it may be that they take the (extremely common) view that the household income is a shared resource. Why should the OP's husband be able to unilaterally OK a large expenditure? This is totally appalling. The final say doesn't rest with the parent, it rests with the couple. If one of them vetos a completely optional luxury purchase, I'd actually say that was good enough!
My own DH is a part-time SAHD/part-time employee, finishing a course. I am more or less the sole earner (his PT income is negligible and more related to training than income). In what universe would it be fair for him to decide to spend a large chunk of my earnings, our budget, on a gift for his adult child? Not in my universe, I can tell you that! (and for that matter, we discuss any^ large purchase, whether for ourselves or for one of the children.)
Interestingly, there was a very recent thread on here regarding the division and use of household finances for children, and the consensus was deafening. But now it involves a stepparent, it appears some people can't see beyond that.