  In order to backward integrate the orbits of Milky Way (MW) dwarf galaxies,
much effort has been invested in recent years to constrain their initial
phase-space coordinates. Yet equally important are the assumptions on the
potential that the dwarf galaxies experience over time, especially given the
fact that the MW is currently accreting the Large Magellanic Cloud (LMC). In
this work, using a dark matter-only zoom-in simulation, we test whether the use
of common parametric forms of the potential is adequate to successfully
backward integrate the orbits of the subhaloes from their present-day
positions. We parametrise the recovered orbits and compare them with those from
the simulations. We find that simple symmetric parametric forms of the
potential fail to capture the complexities and the inhomogeneities of the true
potential experienced by the subhaloes. More specifically, modelling a recent
massive accretion like that of the LMC as a sum of two spherical parametric
potentials leads to substantial errors in the recovered parameters of the
orbits. These errors rival those caused due to a) a 30\% uncertainty in the
virial mass of the MW and b) not modelling the potential of the recently
accreted massive satellite. Our work suggests that i) the uncertainties in the
parameters of the recovered orbits of some MW dwarfs may be under-estimated and
that ii) researchers should characterise the uncertainties inherent to their
choice of integration techniques and assumptions of the potential against
cosmological zoom-in simulations of the MW, which include a recently-accreted
LMC.
