In Hyme's previous negotiation with Ishtalica they got a hold of their princess because at the time Ishtalica was in a position of weakness. Unless they believe that this situation has changed, it makes sense that they would act as if they still hold the cards in this negotiation. In fact, the very reason this meeting was called was precisely because the prince sent a letter with various unacceptable terms, so their behaviour in this meeting is in line with that letter.
When they responded to that letter, they demonstrated to Elena that Ishtalica had more information on the happenings in Hyme than Hyme themselves had (Elena's maid was literally a spy for Ishtalica), while Elena commented that they themselves didn't have such information on Ishtalica and the prince had to bribe his way to send a letter through another country. So yeah, they don't have the spying capabilities to determine the true military might of Ishtalica, and so Hyme's royalty is completely unaware of the true balance of power.
What they do know is that all of Ishtalica's technology runs on resources provided by Hyme. In case of a conflict, they could expect to severely cripple Ishtalica by denying access to these resources and this would eventually even out the playing field.
Of course, there's no wisdom in acting as arrogantly as they are, but it's not really surprising.
Still, this meeting was a bit absurd. They basically cut it short only after a few minutes of exchanges. We'll have to see what Elena's plan is which required letting Hyme's royalty make a poor impression in the first meeting.