An electron electric dipole moment (eEDM) search using laser-coolable triatomics such as YbOH is one of the most sensitive probes for physics beyond the standard model. The eEDM-induced energy shift is proportional to the polarization (P) of the molecule. Similarly to diatomics with an ω-doubling structure, it was assumed that for triatomics with an l-doubling structure, related to the vibrational angular momentum, P can be easily saturated to almost 100% with a moderate external electric field. We developed a method for the calculation of the properties of triatomic molecules and applied it to a calculation of P of YbOH174 in the first excited v=1 bending mode. Calculations showed that most of the levels reach less than 50% efficiency. We showed that this fact is related to the Hund's case b coupling scheme of YbOH. As the coupling scheme (for ω=1/2 molecules) approaches the a (or c) case, polarization increases up to 100%. The results of our calculations should be used for the correct extracting of the eEDM value from YbOH experiments and similar calculations are required for other molecules.