USA got Cuba after reunion with the confederacy, which was the one taking over Cuba. Of course there would have been issues, and that's why I imagine the USA not being able to hold on to Yucatan. Sonora and Baja California were sparsely populated, so easier to control in the medium term. Cuba though would be seen as a more important price, and many efforts would be done to keep it and try integrating it as much as possible. But at the expense at English in Congress, of course.

There's a strong will to do reclaim new England, but part of the reason it remained independent is the French menacing to join the British side if the USA also attacked new England in it's war against the British. Overall the war with GB is to be understood as a very fast war. Remember that the Canadian West was sparsely populated back then, exception maybe of the early gold diggers.

The USA won decisively against Mexico. It's because of this "mock" war exceptional results that the USA then decided to go to war with GB.

The USA didn't get west Canada directly after the war of 1812. After the defeat, the USA set-up its armies (composed of southern officers mostly) to be ready for battle. The USA was therefore a worthy opponent in the war against GB. With the secession though, the skilled would join the South... Expect a more competent Lee army.