The influence of growth conditions to the magnetic microstructure and the parameters of the stress state of LaGa-substituted yttrium iron garnet epitaxial films is analysed. As proved, there are two magnetically non-equivalent tetra-coordinated positions of Fe$^{3+}$ ions with different values and orientations of effective magnetic fields on nuclei for an unsubstituted YIG/GGG film. The appearance of these fields is due to a violation of the anion sublattice stoichiometry and an introduction of impurity atoms into the crystal structure from a melt solution during the growth process. The quantitative characteristics of the dipole-dipole interaction between the $^{57}$Fe nuclei in the garnet structure are obtained experimentally if the Ga$^{3+}$ ions appear in their immediate surroundings. In addition, the change in the orientation of the resulting magnetization vector depending on the magnitude of the diamagnetic substitution is observed. As found, the relatively higher values of period of a stripe domain structure are typical for films with relatively higher values of the component $\epsilon_{zz}$ of the strain tensor when the compression stresses prevails. As established, the increasing of the domain structure period is observed for samples grown at values of the degree of supercooling of $\Delta T$ = 23–24 K. The phenomenological model of the interconnection of the stress state of films and the parameters of its domain structure is proposed.