The PCM/ECM receives input from various sensors and uses this information to control the transmission's solenoids, which in turn control the transmission's shifting. There isn't a separate relay specifically for the transmission solenoids that you can easily locate and replace. Problems typically stem from issues *within* the PCM, faulty transmission solenoids (requiring transmission disassembly), or related wiring harnesses.
To troubleshoot transmission problems, you'll need to consult a repair manual specific to your 1993 Dodge Caravan's engine and transmission. A diagnostic scan tool capable of reading transmission codes is essential. A mechanic with experience working on Chrysler vehicles from that period will be best equipped to diagnose and repair transmission problems.