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Any errors in this sentence?

In the first sentence, this is what you are trying to say. I am not sure if you think the police should be harsh or assume that the police is harsh on those who drink and drive. I went with the first assumption:

"I think/opine that the police should be hard on those who drive drunk(alt: drink and drive), even if they are short on staff."

Second it should be drunk not drunken, I am not sure about the grammar, but drunk sounds right

He drove the car drunk.

I think this is what you are trying to say:

"I believe that the police should be hard (alternative: harsh) on those who drive drunk (alternative: drink and drive), even though they are short-staffed."

Adding the word 'while' makes the sentence sound a little more natural and makes it flow better, but isn't necessary for the sentence to be grammatically correct:

"He drove the car while drunk."

I hope this helps! :)