A theory of electronic properties of a spin-singlet quantum Hall droplet at filling factor nu=2 in a parabolic quantum dot is developed. The excitation spectrum and the stability of the droplet due to the transfer of electrons into the second Landau level at low magnetic fields and due to spin flip at the edge at higher magnetic fields are determined using Hartree-Fock, exact diagonalization, and spin-density functional methods. We show that above a critical number of electrons N(c) the unpolarized nu=2 quantum Hall droplet ceases to be a ground state in favor of spin-polarized phases. We determine the characteristic pattern in the addition and current-amplitude Coulomb blockade spectra associated with the stable nu=2 droplet. We show that the spin transition of the droplet at a critical number of electrons is accompanied by the reversal of the current-amplitude modulation at the nu=2 line, as observed in recent experiments.