indeed if i am not mistaken Diaz constructed the Tehuantepec railway over the abandoned canal observation areas.There were three routes considered for the canal OTL. One through Nicaragua, one through Panama and the third through Tehuantepec (in Mexico itself). Abd between 1857 and 1882 there was a lot of work done on the Tehuantepec route.
If i am not mistaken, Maximilian I otl wanted to have a baby girl and engage her to one of the Iturbide boys to create a new royal house, something called the House of Habsburg-Iturbide to unite the two houses and create dynastic stability. So if Maximilian I does have a baby girl by Carlotta, then that's a possibility.You see all kinds of petty defiance from client states, which the Second Mexican Empire definitely was. In the Warsaw Pact it was routine even though they all backed the Soviets militarily without hesitation when it mattered. The same kind of friction existed between the US and South Vietnam over dozens of issues. Colonial powers often got lip from their client chiefdoms.
That's why there's a difference between outright annexation/colonization and installing allies in power. Each has pros and cons for the great power doing it. In the case of Mexico, the Empire and the French intervention were based in the conservative elements of society, even though Maximilian had a vision to break out of that narrow set of expectations somewhat with his liberal conservatism. That works out just fine for the French, because if the Hapsburgs want to keep the throne against the conservatives, who will want to install the Iturbides after Maximillian, they will have to lean on French influence permanently.
the US never brought up the notion of direct interference in Mexico OTL even in 1865 when the Imperials were winning and the USA was still massively mobilized. The public was just not in favor of a war.The only question is would the United states allow that action. Would they allow a strong mexico, sure Maximilian might do that but the united states can always send supplies at the border to fund and arm the Juaristas. And when the French get out of Mexico in otl the Imperialistas forces are doomed against the modernized Juaristas. Would the united states allow a french client state or a latin american power going strong