  We perform full two-dimensional (2D) numerical relaxations of isospinning
soliton solutions in the baby Skyrme model in which the global $O(3)$ symmetry
is broken by the 2D analogue of the pion mass term in the Skyrme model. In our
calculations we explicitely allow the isospinning solitons to deform and to
break the symmetries of the static configurations. We find that stable
isospinning baby Skyrme solutions can be constructed numerically for all
angular frequencies $\omega\le \text{min}(\mu,1)$, where $\mu$ is the mass
parameter of the model. Stable, rotationally-symmetric baby Skyrmion solutions
for higher angular velocities are simply an artefact of the hedgehog
approximation. Isospinning multisoliton solutions of topological charge $B$
turn out to be unstable to break up into their $B$ charge-1 constituents at
some critical breakup frequency value. Furthermore, we find that for $\mu$
sufficiently large the rotational symmetry of charge-2 baby Skyrmions becomes
broken at a critical angular frequency $\omega$.
