  We study the spin-spin interaction between quantum dots coupled through a two
dimensional electron gas with spin-orbit interaction. We show that the
interplay between transverse electron focusing and spin-orbit coupling allows
to dynamically change the symmetry of the effective spin-spin Hamiltonian. That
is, the interaction can be changed from Ising-like to Heisenberg-like and vice
versa. The sign and magnitude of the coupling constant can also be tuned.
