IF the trans is slipping that much when it's hot, then the fluid should be turning browner than the "good" dark red cooler. Plus the normal pungent smell should also becoming more "cooked", too.
When first started in the morning, it is normal, when started in "P", for it to take a second or two before the car moves as the torque converter is refilled by the trans pump. But this only happens on the first start of the day. Better to start it in "N" to minimize such laziness (which generally starts when the factory-fill fluid is changed for the first time in the car's life, by observation).
When the trans "slips" once everything's warmed up, does the car not move from a stop when the engine speed is increased? Only momentarily? Or does it feel like the trans is in "N" and then catches hold?
A fluid change with your trans fluid of choice (the old spec was the same as GM Dexron, as in what became "Dexron III", but Ford Type F might make the shifts a bit firmer. The newer Dexron VI is a syn fluid, which is better and more costly. A new Dexron III equivalent might work just fine (now "Multi-Make" in most brands, so read the bottle to see that the main application is for GM Dexron III). Not sure about the newer Chrysler "ATF+__" fluids in the older TorqueFlites.
First thing would be to get the fluid/filter changed.
Just some thoughts,
CBODY67