We consider the problem of quantizing a Skyrmion which is allowed to vibrate, rotate and isorotate. Previous approaches have neglected the interactions between vibrations and zero modes (analogous to so-called Coriolis terms in the molecular physics literature). A new formalism incorporating these interactions is introduced, inspired by a principal bundle approach to deformable-body dynamics. We quantize the $B=4$ and $B=7$ Skyrmions and compare the results to observed nuclear properties of Helium-4 and the Lithium-7/Beryllium-7 isospin doublet.