Here's my opinion:

You were in a stressful and confusing situation where something that was of the utmost importance to you and your partner was being processed.

Quite naturally you wanted to be sure of there being no chance that things could go wrong, causing future problems, and THAT is why you decided to pay the extra money for the checking process.

Under the circumstances I would expect a public employee who had been correctly trained and carefully selected for their 'public relations' skills to have handled the situation in a calm, polite and professional manner.

From what you have said, that certainly does not appear to have been the case.

I don't care if she had processed a hundred such cases that morning. That is no excuse.
There are plenty of suitable people currently unemployed and more than happy to pick up her baton.