The controversy "dark matter vs. modified gravity" constitutes a major topic of discussion. It was proposed that dynamical friction could be used to discriminate between the two alternatives. Analytic calculations indicate that, with modified gravity, globular clusters (GCs) of low-mass galaxies experience much stronger dynamical friction than in the equivalent system with Newtonian gravity and dark matter. As a result, in modified gravity the old GCs of low mass galaxies should have already settled in the centers of the galaxies. This is not observed. Here we report on our efforts to verify the analytic results by self-consistent simulations with the MOND-type (modified Newtonian dynamics) gravity. The core stalling mechanism, that was not considered in the analytic calculations, prevents GCs to settle in centers of ultra-diffuse galaxies. For isolated dwarf galaxies, which are gas-rich objects, supernova explosions prevent the GCs from settling.