  We study the short-time distribution $\mathcal{P}\left(H,L,t\right)$ of the
two-point two-time height difference $H=h(L,t)-h(0,0)$ of a stationary
Kardar-Parisi-Zhang (KPZ) interface in 1+1 dimension. Employing the
optimal-fluctuation method, we develop an effective Landau theory for the
second-order dynamical phase transition found previously for $L=0$ at a
critical value $H=H_c$. We show that $|H|$ and $L$ play the roles of inverse
temperature and external magnetic field, respectively. In particular, we find a
first-order dynamical phase transition when $L$ changes sign, at supercritical
$H$. We also determine analytically $\mathcal{P}\left(H,L,t\right)$ in several
limits away from the second-order transition. Typical fluctuations of $H$ are
Gaussian, but the distribution tails are highly asymmetric. The tails
$-\ln\mathcal{P}\sim\left|H\right|^{3/2} \! /\sqrt{t}$ and
$-\ln\mathcal{P}\sim\left|H\right|^{5/2} \! /\sqrt{t}$, previously found for
$L=0$, are enhanced for $L \ne 0$. At very large $|L|$ the whole
height-difference distribution $\mathcal{P}\left(H,L,t\right)$ is
time-independent and Gaussian in $H$, $-\ln\mathcal{P}\sim\left|H\right|^{2} \!
/|L|$, describing the probability of creating a ramp-like height profile at
$t=0$.
