We present both experimental magneto-optical measurements and a theoretical analysis of polaron anomalies observed when impurity electron excitations are resonant in energy with two long-wavelength LO phonons. Specifically, we have measured the first harmonic of impurity cyclotron resonance (HCR) and the LO-phonon assisted cyclotron resonance transition (LOCR) in InSb in the magnetic field range 27-60 kG. In this range the HCR is nearly twice the LO-phonon energy, and the LOCR is close to the HCR. When the magnetic field is swept through this range, we have observed dramatic polaron pinning effects that are quite different from those ordinarily observed in the one LO-phonon region. For example, the line intensity of the LOCR anomalously disappears in the resonant interaction region but regains its intensity at either lower or higher fields. This feature is just opposite to the polaron pinning effects in the one LO-phonon region. In addition, we have calculated the magneto-optical spectrum of donor-impurity electrons taking into account nonparabolicity, impurity-electron energy-level scheme, and polaron interactions between the HCR, LOCR, and the lowest set of impurity states with participation of up to two LO phonons. We demonstrate that by using the nonparabolic-energy-level scheme, the wave functions of donor electrons, and the known Fr\"ohlich interaction constant between electrons and LO phonons, we can explain the anomalous features of the present data quantitatively without any adjustable parameters.