The dynamics of point vortices in a plane is a an example of a Hamiltonian system with symmetry SE(2). In this, the vortices do not have the attribute of mass but rather move according to a Hamiltonian and a symplectic form obtained from the two plane coordinates (rather than from position and momentum as in a Lagrangian system). The (momentum dependant) symplectic reduced spaces of the non-abelian and non-compact symmetry SE(2) have varying dimension. We find a regularized reduction and realize perturbation from non-generic to generic momentum as Hamiltonian SO(2) symmetry breaking on a fixed symplectic manifold. In the case of four vortices the reduced dimension is four and stability should follow from the usual normal form and Moser-twist theorem.