Umm, no; Mexico had been an independent country for over 20 years prior to the Mexican-American War. Even a the time of the war, many in the US opposed the war as a war of conquest.
Per our Constitution, the US recognized the claim of NO Monarch on the N. American continent.
Good lord, do you have a muddled conception of US History. There's not word one in the Consitution about ANY such matters. You're thinking of the Monroe Doctrine but you're even sort of twisting that.
Also, the war of 1812, among other things, was fought to keep British press gangs OFF us shipping. Am I wrong there too?
That's the "official" reason and the sanitized children's textbook reason.
However, the British actually ended that practice right after we declared war (before they knew we had declared war, and we didn't get the news of it till after we'd declared war.)
And virtually all of the impressed seamen were from New England.
The vote for war was actually close; all the New England congressmen voted AGAINST going to war, even though the only people being impressed were their constituents. It was the Western states that voted for the war; they had a lot of people that wanted to conquer Canada.
In fact there was so much opposition to the War of 1812 in New England there was a meeting to discuss Secession from the US.