Unitals in $PG(2,q^2)$ with a large 2-point stabiliser

Let $\cU$ be a unital embedded in the Desarguesian projective plane
$\PG(2,q^2)$. Write $M$ for the subgroup of $\PGL(3,q^2)$ which preserves
$\cU$. We show that $\cU$ is classical if and only if $\cU$ has two
distinct points $P,Q$ for which the stabiliser $G=M_{P,Q}$ has order
$q^2-1$.