Do you think the king and queen want to see a successful relationship blossom between Hamlet and Ophelia, or do you think they simply want Hamlet to stop misbehaving and if Ophelia can temporarily appease him, so be it?

The queen and the kings do not want to see a successful relationship between Hamlet and Ophelia thinking and fearing that Hamlet is not earnest to her.

Explanation:

When Polonius found out that Hamlet is love stick to his daughter Ophelia, he wanted an end to it, such that he approached Claudius the new king of Denmark for an idea on how to go about it.

Both men agreed on eavesdropping on their conversation anytime they stay together.