I really want iris to bring up how by marrying yuri. The second prince is basically giving up his claim for the throne - the issue about who will succeed the kingdom revolves around how the true queen is a barons daughter, but the second, living queen is the daughter of a duke. By marrying yuri, the second prince is either announcing that a) he acknowledges that social status and titles don't matter, and whoever he marries first should be the rightful queen and their children the heir, or b) that he plans to take on a wife of higher nobility, who he will place above yuri as the true queen, with the newer duke's daughter's children being the rightful heir.
By situation a's logic, the first prince should be king. The second prince, and especially his mother are far too selfish give up money and power for so called 'love'. I feel like the second prince would, in this scenario, break his engagement with yuri so he stands at least a fighting chance of inheriting the throne.
In scenario a, if Yuri is actually evil, or at least selfish and self aware of how her spending hurts the country, would also realise that if he marries her, he would have to accept this logic, and would no longer have the power and money to sustain her spending habits. In his scenario, I think she would wait for the prince to cancel his engagement with her, then run to the next most secure and rich boy in her crew.
If she's not self aware though, then I think that she might cling to the prince, not give him the chance to cancel their engagement, and ruin them both by spend all their money.
In scenario b, if yuri is self aware, I think she would defend the prince, and stop the conversation there before he can admit it so that she can still at least keep money and power until he take s on a new wife, then deal with the new wife then, where as if she's not self aware, I think she'll just run off crying, and leave them all standing around.