I have been contemplating these two imperative constructions for the past several days.

Question:
Are both constructions correct?

Explanation:
The verb “Give” in either construction is the imperative verb.

The phrase “the money” in either construction is the direct object.

The pronoun “us” in either construction is the indirect object.

In other words, the speaker of the sentence is telling the listener to take an action (“Give”) with a direct object (“the money”) on behalf of an indirect object (“us”).

So you might wonder why the preposition “to” is required in one construction and is NOT required in the other construction.

According to the discussion about the dative case in English at Wikipedia, the indirect object of an action does not have to be expressed with a preposition such as “to” or “for”.

In other words, the objective pronoun “us” may immediately follow the main verb and be used in a dative manner, as long as that verb has a direct object, too.

So the preposition “to” in “Give to us the money!” is optional in current English usage.

This gives [to] us the answer to the original question.

Answer:
Yes, both constructions, along with “Give to us the money!”, are correct.