The dynamics of interacting quantum vortices in a quasi-2D spatially nonuniform Bose-Einstein
condensate is considered in hydrodynamic approximation for the case when equilibrium density of
the condensate vanishes at two points of the plane, in each of them the presence of a stationary vortex
of several quanta of circulation is possible. A special class of the density profiles is chosen,
so that with the help of a conformal mapping of the plane onto a cylinder, analytical calculation becomes
possible for the velocity field created by vortices. Equations of motion are presented in a noncanonical
Hamiltonian form. The theory is generalized to the case when condensate takes form of a curved quasi-2D
shell in the 3D space.