Hey herricks, it seems to me that you are looking for an America where the Federalists (and particularly Alexander Hamilton and his allies) are in power. They wanted America to side with Britain against France, and they advocated a stronger army and navy. Hamilton exerted influence during the Washington and Adams administrations, but the 'Jeffersonian revolution' of 1800 meant that the Democratic-Republicans seized power, and they were subsequently in charge for a good long time.
This may help you get the results you want:
- Get a strong, capable Federalist to be Washington's vice president, instead of John Adams. That Federalist can then become president when Washington retires, and start pushing for a stronger navy and/or army. Hamilton himself would ideologically be the perfect candidate, but he's a very difficult guy. He'll make enemies, which is not what you want. You might alternatively consider John Jay, John Marshall, Thomas Pinckney or Charles Cotesworth Pinckney.
- Keep Jefferson in France. Or kill him off early. Something like that. He basically was the Democratic-Republican Party. Patrick Henry, who started out as an avowed anti-federalist, ultimately went over to the Federalists. James Madison was intially a Federalist, and went over to the Jeffersonians. Without Jefferson, you can plausibly keep him a Federalist.
- Then make the Democratic-Republican Party field a weak candidate in 1800. George Clinton, maybe? If the Democratic-Republican Party can be discredited by some scandal or political mess-up, that's a bonus. The Federalist candidate gets elected instead. Supports Britain against France.
- Eventually, the public gets tired of the Federalist government, and a Democratic-Republican gets elected. It happened in 1800 IOTL, suppose it happens in 1808 or 1812 ITTL. From there, you can set the stage for a dimplomatic reversal, wherein the US turns against Britain. That eventually leads to war with Britain, and there you go: all your aims have been achieved.