2003 Dodge Stratus Leaking transmission module

Can you please verify what you were told. Your transmission control module is no where near the transmission or is capable of leaking any fluid. Your TCM is located under the hood, next to the power distribution center.

If in fact your transmission is leaking, no one can really tell you how long you have before it breaks. If the leak is small enough (maybe a drip every 10 minutes of driving, you may prolong the inevitable by keeping the fluid level at where it is supposed to be. But if it is leaving a trail of fluid while the engine is running, you don't have any time, at all.