No, our government should be required to go through the other government to get that information. Our government does not have jurisdiction in other countries PERIOD.
True, but irrelevant in cases like this. The US government does have jurisdiction over Microsoft's US operations, and Microsoft's US operations have the ability to retrieve the information from Microsoft's servers in Ireland. The mere fact that the data is in Ireland is no reason that the US company can't be ordered to retrieve the data they control and have access to.
Similarly, if you were being investigated for a crime you could be required by the courts to turn over the records of you Swiss bank account. The court couldn't issue orders to the Swiss bank (though they could make a request, which the bank might choose to honor, or they could ask the Swiss authorities to issue an order to the bank, which the bank would have to honor if the Swiss government chose to cooperate), but it absolutely could issue orders to you, a US person in the US, and your failure to comply would result in you being held in contempt of court, and jailed or otherwise punished until you do comply.