PART I

To the second question, in diaries, yes, but in person, we don't know. To the first, though, Hamilton's dreams weren't as much about expansion (not that he minded it) as they were him leading an army and becoming President.

The scene that you link seems to be inspired from a meeting that Adams had with Hamilton in Trenton in the middle of October 1799, related by McCullough in his book that's used as the basis for the HBO series. But to get there, we need to go back a bit to explain the background of the relationship between the two men, the policy debate at the time, and the reason for Hamilton's aggressiveness.

Hamilton does not like Adams from relatively early on; it's unclear precisely when and why this starts on his end, although a reasonable guess is that it's split between him never fully trusting Adams to carry out the Federalist agenda as well as seeing him getting in his way as a political rival. Hamilton starts by trying to lobby various electors in the 1788 race to make sure Adams doesn't have a chance of tying Washington (remember, this is pre-Twelfth Amendment and they're on the same ballot), and in fact peels off more than half of the vote. During this, Hamilton explains privately that he's not against Adams per se - "Mr. A, to a sound understanding, has always appeared to me to add an ardent love for the public good - but that this is out of respect for Washington, who he fears is going to not have a loyal second-in-command given that Adams had problems working with Franklin, his senior in Paris. (The same concern is voiced by Madison, incidentally.) Adams is hurt by the lukewarm support of his countrymen, but is generally unaware of Hamilton's role. Hamilton helps Adams in 1792, more because he's more concerned with Aaron Burr than anything else.

Then comes 1796. It's a strange election on multiple levels. First, Washington holds off on announcing his plans until two months before the election, when Hamilton ghostwrites his Farewell Address into what's widely regarded then as a campaign speech to rally supporters of his administration. Second, it's the first one where parties play a role, even if they're mostly proto-parties and sectional at that point. There's some scholarship that suggests there were consistent voting patterns in 1793, and you can even see more of it in some actions of the First Congress in 1789, but the Jay Treaty in 1794 is generally regarded as the first out-and-out brawl that precipitates the advent of the first party system. Jay jokes that he could navigate all the way to the Mississppi by the light given off by burning effigies along the way, and it's forced through by a 20-10 proto-party margin on a secret vote; Burr essentially becomes the first Senate Minority Leader as a result.

Third, given this, there's no formal selection process that produces Adams versus Jefferson; it's debated internally among the proto-party leaders - mostly members of Congress caucusing - but Adams gets the hint in the spring and tells his wife that 'the Federalists had no thought of overleaping the succession.' Jefferson has been fully retired at that point for 3 years - he'd gotten tired of Washington ignoring his advice, but even more so of having to sit through the legendary multiple hours of bloviating by Hamilton as he lost battle after battle with him in Cabinet - but is lured out of it by both boredom and that he doesn't like the way the future looks under the Federalists. Both are lousy options for Hamilton, who thinks he'd be a better choice, but he's also someone who really does not want Jefferson coming back into public life and realizes that for a variety of reasons he doesn't stand a chance if he goes up against either directly. The Jeffersonian Republicans choose Aaron Burr relatively quickly, but the Vice Presidential nomination for the Federalists gets very complicated.

That's because Hamilton is working behind the scenes to get Thomas Pinckney of South Carolina elected not Vice President but President outright despite Adams being anointed as the preferred candidate. If Pinckney can peel off a few Southern second place votes (Adams is wildly unpopular in parts of the South, and Jefferson-Pinckney is what Hamilton aims for there) and if Northern Federalists can be convinced to vote a straight Adams-Pinckney ticket, there's a decent shot Adams gets 'accidentally' a few votes less than Pinckney and Hamilton has someone who is far easier to control and more firmly in line with High Federalism.

Neither the Adams-Pickney New England strategy of Hamilton nor the idea of putting a northerner on the ticket to balance out the Virginians work well. Pickney does come in third with 59 votes - he splits tickets in the South - but in New England he only gets 21 out of 39 possible electors; if he'd gotten 34 he indeed would have beat both Adams and Jefferson. On the other hand, Burr gets outright rejected by the Virginia delegation, receiving only 2 of their 21 votes, which he takes very personally - and plays a role in his conduct 4 years later.

But Adams makes a critical mistake that gives Hamilton significant leverage over his administration anyway, and that's what I'll talk about in a few hours when I get to Part II.