We study the complex collective dynamics mediated by flow resistance interactions when trains of non-coalescing and coalescing confined drops are introduced into a microfluidic parking network (MPN). The MPN consists of serially connected loops capable of parking arrays of drops. We define parking modes based on whether drops park without breakage or drop fragments are parked subsequent to breakage or drops park after coalescence. With both non-coalescing and coalescing drops, we map the occurrence of these parking modes in MPNs as a function of system parameters including drop volume, drop spacing and capillary number. We find that the non-coalescing drops can either park or break in the network, producing highly polydisperse arrays. We further show that parking due to collision induced droplet break-up is the main cause of polydispersity. We discover that collisions occur due to a crowding instability, which is a natural outcome of the network topology. In striking contrast, with coalescing drops we show that the ability of drops to coalesce rectifies the volume of parked polydisperse drops, despite drops breaking in the network. We find that several parking modes act in concert during this hydrodynamic self-rectification mechanism, producing highly monodisperse drop arrays over a wide operating parameter space. We demonstrate that the rectification mechanism can be harnessed to produce two-dimensional arrays of microfluidic drops with highly tunable surface-to-volume ratios, paving the way for fundamental investigations of interfacial phenomena in emulsions.