Apart from a sub par buildup (2 episodes of snow, Ramsay's night raid ... it's just not enough for one to grasp the direness of the situation ... it was too fast), I think everything's there. The show established that Stannis loves his daughter. It also established that Stannis will do anything to get what he wants (or rather, to do his duty). Apparently he decided that his duty to the realm outweights his duty to his lineage. That said, I don't think his decision puts his heartfelt conversation with Shireen (from a few episodes ago) out of place. If anything, it just increases the magnitude of his sacrifice and the difficulty of his decision (thanks to Stephen Dillane's layered performance, the difficuty itself is apparent).
At the end of the day, I can't picture Shireen being burned. I can't imagine the screams, I can't imagine her being tied to a stake. So for this reason (which, admiteddly, isn't much of a reason) I doubt she'll be sacrificed.
I've read the alleged synopsis for E9, tho, and it says something along the lines of: "Stannis faces a difficult decision." So I believe that will be the make it or break it for her (and her father). I suppose we'll find out in two weeks.
Tbh, I don't really imagine Stannis saying anything after being turned down. Less so pleading for gold. Stan is imo not the person to ask for stuff. Sure, he'll go out of his way to make a point that something belongs to him (Storm's End (to Robert)/7 Kingdoms (to the rest of Westeros)), but this is not really the case here. And besides ... there were theories Stan had Asperger's. Him freezing when he has to ask people (he doesn't know and are not in any way inferior or in debt to him) for their help is something I can easily see happening.