  We study spin dynamics for two electrons confined to a double quantum dot
under the influence of an oscillating exchange interaction. This leads to
driven Rabi oscillations between the $\ket{\uparrow\downarrow}$--state and the
$\ket{\downarrow\uparrow}$--state of the two--electron system. The width of the
Rabi resonance is proportional to the amplitude of the oscillating exchange. A
measurement of the Rabi resonance allows one to narrow the distribution of
nuclear spin states and thereby to prolong the spin decoherence time. Further,
we study decoherence of the two-electron states due to the hyperfine
interaction and give requirements on the parameters of the system in order to
initialize in the $\ket{\uparrow\downarrow}$--state and to perform a
$\sqrt{\mathrm{SWAP}}$ operation with unit fidelity.
