My wife recently purchased a 1990 Plymouth Sundance that was owned by a little old lady that drove back and forth to the grocery store. Unfortunately this car's shifting characteristics best suit her, not my wife.
Is a simple adjustment all that is needed to make this car shift more aggressively or am I looking at major work? In the interest of bettering my hands-on education, is it wise for me to make these adjustments or should I step away from this job?
You most definitely should get a professional diagnosis before getting your hands dirty. Yes, there is an adjustable Throttle Pressure Cable that will affect the transmission's shift timing and feel. It can be adjusted to confirm it's at the manufacturer's specifications, but varying from that is not recommended.
It may be a significant internal transmission failure or perhaps something as simple as a clogged fuel filter which can cause engine power loss along with an erratic shifting transmission.
If you're describing the normal operation of grandmas' Sundance, I would strongly advise against any modifications. A high performance shift kit in this transmission would not be a good idea.