  We study ultracold long-range collisions of heteronuclear alkali-metal dimers
with a reservoir gas of alkali-metal Rydberg atoms in a two-photon laser
excitation scheme. In a low density regime where molecules remain outside the
Rydberg orbits of the reservoir atoms, we show that the two-photon
photoassociation (PA) of the atom-molecule pair into a long-range bound trimer
state is efficient over a broad range of atomic Rydberg channels. As a case
study, we obtain the PA lineshapes for the formation of trimers composed of KRb
molecules in the rovibrational ground state and excited Rb atoms in the
asymptotic Rydberg levels $n^{2}S_j$ and $n^{2}D_j$, for $n=20-80$. We predict
atom-molecule binding energies in the range $10-10^3$ kHz for the first
vibrational state below threshold. The average trimer formation rate is order
$10^8\, {\rm s}^{-1}$ at 1.0 $\mu$K, and depends weakly on the principal
quantum number $n$. Our results set the foundations for a broader understanding
of exotic long range collisions of dilute molecules in ultracold atomic Rydberg
reservoirs.
