Mr. Trump and his spokesperson seem to favor the word OUR, as in our great military or our nation when THE nation might do. Is there a signal or purpose for this usage?
With regard to inclusiveness, Winston Churchill did much the same seventeen days after taking over as Prime Minister on the 10th of May, 1940 (eight months after the beginning of the Second World War) when he made a brief statement to the Commons on 28 May reporting the Belgian capitulation, and concluding:
Meanwhile, the House should prepare itself for hard and heavy tidings. I have only to add that nothing which may happen in this battle can in any way relieve us of our duty to defend the world cause to which we have vowed ourselves; nor should it destroy our confidence in our power to make our way, as on former occasions in our history, through disaster and through grief to the ultimate defeat of our enemies.
Having spoken to the House of Commons, thus, and having assumed their unity of purpose he then included not only the people of Great Britain but the nations which (at that time) encircled the globe in Commonwealth:
We shall go on to the end. We shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our island, whatever the cost may be. We shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender [...].
Then, including the 'Empire' and also the 'New World' - meaning the USA in particular - he continued:
and if, which I do not for a moment believe, this island or a large part of it were subjugated and starving, then our Empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle, until, in God's good time, the New World, with all its power and might, steps forth to the rescue and the liberation of the old.
You ask 'is there a signal or purpose' to the present inclusiveness expressed by POTUS ? And that is why I have quoted Winston Churchill at length for the world faces a far more destructive force now than it did in 1939-45.
Now, by using technology that has become all too accessible, a rogue state threatens the entire globe and attempts to push the whole of humanity towards an unthinkable precipice, while those closest to it seem reluctant to repress such ambitions.
And its solicitations regarding Olympic Games could as well be an attempt to drive a wedge between the whole peninsula and the rest of the world, or as well be a mere truculent response to sanctions, than they might be a genuine step towards a better peace.
I think that the President of the United States (whoever that happens to be at the present time) is quite right to attempt to gather the USA into one and is quite right to seek international allies in order to maintain the balance of power in this most dangerous world in which we live.
He is being precise.
There are in fact many great militaries, and many nations in the world, and while from context it is unlikely that Trump is referring to any other than the US, he is more technically clear in saying "our" rather than "the". Especially if you realize that some of Trump's listeners are international. Reminding people that they are part of the nation never hurt a politician either.