What makes american federalism especially intricate?

The United States (addressing the 50 states) actually does not have an especially intricate form of Federation. Federation is symmetric (other Symmetrical Federations include Germany and Switzerland.) This means that the political subdivisions known as states or cantons existing within the nation-state all have the same basic relationship with the central/federal government, in which the basic law (constitution) applies. Although the indigenous/native American tribal lands and reservations are pockets of land in which constitution does not automatically apply. Asymmetrical Federations (such as Russia and Canada) have members of the Federation that may have special autonomy (and all sorts of various levels of association) such as in Russia with federal cities of Moscow and St. Petersburg, oblasts, okrugs, autonomous republics, and republics within the political subdivision that are all part of Federation.

The US has a number of political subdivisions that have varying degrees of organization with the central government. The case of the native American reservations is laid out in precedents, but US overseas possessions and the federal district that is Washington, DC are different in that constitution does not automatically apply but inhabitants enjoy citizenship or in the case of American Samoa, US nationality status. However, when we consider the cases like Puerto Rico, Guam, US Virgin Islands and Washington, DC and other inhabitants of territories have limited representation in Washington, DC and do not vote for the Presidential candidates. These territories have their own central political organization which may decide to leave by opting for independence or they may seek to join the Federation with full statehood which requires both central government bodies consensus.

There are a few final things we need to talk about, and that includes the Palmyra Atoll and then the Compact of Free Association. If a bizarre incident where a person is born on the Palmyra Atoll, it would mean that it would become a state and the population of 1 now would be entitled to full representation (1 representative, 2 Senators, 3 electoral college seats) in Washington, DC. finally the compact of free association in which the Marshall Islands, Palau, and the Federated States of Micronesia enjoy economic and security/military services from Washington DC, and free migration processes but are foreign countries with their own UN Membership.

It is symmetrical Federation, but incredibly complicated. But otherwise it's America.