It's about as believable as the Sansa-Arya tension from last season.

Danaerys is being ridiculous because it serves the shows interest in giving a plausible motive for Jon to want replace her. All we the viewers have to do is ignore that she's behaving totally out of character.

Danaerys showed more charm trying to get the Khals to follow her before burning them. This is honestly just stupid.

They will almost certainly resolve all this in an episode or two. But it is all really unbelievable. What stops Sansa from asking Bran to look into Dany's past actions as a way to get the measure of her?

What stops Dany from asking Jon and Tyrion about Sansa for the same reason?

Nothing, except the need to create the idea they're opposed to each other, when they're likely to have the most sympathy for each other for what they've been through.