Nonlinear waves that collide with localized defects exhibit complex behavior. Apart from reflection, transmission, and annihilation of an incident wave, a local inhomogeneity can activate internal modes of solitons, producing many impressive phenomena. In this work we investigate a two-dimensional sine-Gordon model perturbed by a family of localized forces. We observed the formation of bubblelike and droplike structures due to local internal shape mode instabilities. We describe the formation of such structures on the basis of a one-dimensional theory of activation of internal modes of sine-Gordon solitons. An interpretation of the observed phenomena, in the context of phase transition theory, is given. Implications in Josephson junctions with a current dipole device are discussed.