I think you have two problems that are both related to the transmission. In your first example, you indicated the van drives fine but when you come to a stoplight, it shudders a bit when you are taking off down the road. And, then you say you see red stains underneath your minivan.
For starters, I think that, at some point, your transmission was overfilled. You may think this is okay, but it isn’t. The transmission is made to run with — depending on the type, clutches and the like — anywhere between three and six quarts of transmission fluid — most use five.
Each transmission has certain pressure parameters to work correctly. In other words, if your transmission normally runs with five quarts of fluid, it might be running at say six pounds per square in inside (don’t hold me to the exact figures here because I’m describing how things work). If you add an extra quart of fluid, you are adding to the pressure load. In other words, the six pounds may now be nine or 10 or so.
At this level of pressure, the various parts don’t work correctly. In fact, they are forced to work against pressures that are too high and, in some cases, parts that should be open are closed and vice versa. At this time, damage begins to accumulate in your transmission.
I speculate that this is what happened to your tranny. Unfortunately, it is too late to do much about it now.
Because the pressure was too high, I think the torque converter and impeller blades have been damaged as have the clutches and bands. The result is the type of whirring style delay you mentioned.
The only cure for either problem is a rebuilt transmission. If you plan to keep the Dodge on the road and it is in good shape — it is 17 years old, after all — then you will have to make the investment of about $3,400 to replace the current transaxle with a rebuilt. Be aware that the overpressure may have forced the output shafts out of true and they may also be damaged so it is something else to think about (you may not notice the problem as your transaxle (transmission) is used to dealing with output shafts that aren’t true so it performs in a way that feels right to you).
As to the second issue, it is related to the first. Since your transmission has been overfilled, seals may have weakened or blown out. Those seals are on the input and output shafts as well as around the transmission pan.
I suspect that if you look under your transmission you will see transmission fluid dripping from the bead edge of the pan.
Again, there’s major damage here that has to be repaired.
Frankly with what you have described to me, maybe it’s time to think of turning in your old ride on something a bit newer. There are great deals around on 2005-10 minivans that offer a lot for the money. I know it isn’t what you may have hoped to hear, but I am being honest. Let me know what you decide.