  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 is determined using Hartree-Fock, exact
diagonalisation, and spin-density functional methods. We show that above a
critical number of electrons $N_c$ the unpolarised $\nu=2$ quantum Hall droplet
ceases to be a ground state in favor of spin-polarised 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.
