With the release of Gaia DR2, it is now possible to measure the proper motions (PMs) of the lowest-mass, ultrafaint satellite galaxies in the Milky Way's (MW) halo for the first time. Many of these faint satellites are posited to have been accreted as satellites of the Magellanic Clouds (MCs). Using their six-dimensional phase-space information, we calculate the orbital histories of 13 ultrafaint satellites and five classical dwarf spheroidals in a combined MW+LMC+SMC potential to determine which galaxies are dynamically associated with the MCs. These 18 galaxies are separated into four classes: (i) long-term Magellanic satellites that have been bound to the MCs for at least the last two consecutive orbits around the MCs (Carina 2, Carina 3, Horologium 1, Hydrus 1); (ii) Magellanic satellites that were recently captured by the MCs < 1 Gyr ago (Reticulum 2, Phoenix 2); (iii) MW satellites that have interacted with the MCs (Sculptor 1, Tucana 3, Segue 1); and (iv) MW satellites (Aquarius 2, Canes Venatici 2, Crater 2, Draco 1, Draco 2, Hydra 2, Carina, Fornax, Ursa Minor). Results are reported for a range of MW and LMC masses. Contrary to previous work, we find no dynamical association between Carina, Fornax, and the MCs. Finally, we determine that the addition of the SMC's gravitational potential affects the longevity of satellites as members of the Magellanic system (long-term versus recently captured), but it does not change the total number of Magellanic satellites.