  We theoretically investigate the orbital effects of an in-plane magnetic
field on the spectrum of a quantum dot embedded in a two-dimensional electron
gas (2DEG). We derive an effective two-dimensional Hamiltonian where these
effects enter in proportion to the flux penetrating the 2DEG. We quantify the
latter in detail for harmonic, triangular, and square potential of the
heterostructure. We show how the orbital effects allow one to extract a wealth
of information, for example, on the heterostructure interface, the quantum dot
size and orientation, and the spin-orbit fields. We illustrate the formalism by
extracting this information from recent measured data [L.~C.~Camenzind, et al.,
arXiv:1804.00162; Nat. Commun. 9, 3454 (2018)].
