  We solve an interpolation problem in $A^p_\alpha$ involving specifying a set
of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative
at the $k^{\textrm{th}}$ point is up to a constant as large as possible for
functions of unit norm. The solution obtained has norm bounded by a constant
independent of the points chosen. As a direct application, we obtain a
characterization of the order-boundedness of a sum of products of weighted
composition and differentiation operators acting between weighted Bergman
spaces. We also characterize the compactness of such operators that map a
weighted Bergman space into the space of bounded analytic functions.
