Transmission swap, 2010 4G TL transmission Fit a 2004 3G?

Looking at the interchange info the 2010 unit is a lot different and doesn't interchange. The control systems changed, and the transmission internals are different as well. As it works in manual mode, I would think the issue is in the electronics. Do you have a scan tool that can look at the transmission controls? It could be as simple as the TCM requiring relearns for the new parts.

That would cause problems as it is the pressure control solenoid A stuck off. So, it doesn't have internal pressure control of and will cause shifting issues.
DTC P0746: A/T Clutch Pressure Control Solenoid Valve A Stuck OFF

NOTE: Record all freeze data and review General Troubleshooting Information before you troubleshoot.

1. Warm up the engine to normal operating temperature (the radio fan comes on).
2. Check to be sure that the transmission is filled to the proper level, and check for fluid leaks.
3. Drain the ATF through a paint strainer. Look for contamination (small pieces of metal or friction material) in the strainer.

NOTE: If little or no contamination is found in the strainer, the ATF is OK. Discoloration, small chips or flakes, metal fuzz and a slightly "burnt" smell is considered normal.

Is the ATF okay?
YES-Replace the ATF, then go to step 4.
NO-Repair or replace the transmission.
4. Clear the DTC with the HDS.
5. Test-drive the vehicle in the D position in ail five gears at speeds over 12 mph (20 km/h) for more than 20 seconds, then slow down to a stop.
6. Retest-drive the vehicle in the D position in all five gears at speeds over 12 mph (20 km/h) for more than 20 seconds, then slow down to a stop.
7. Check the OBD STATUS in DTCs MENU for a pass/fail test of code P0746.
Did the result indicate a fail?
YES-Go to step 8.
NO-Intermittent failure, the system is OK at this time. If the tester indicates NOT COMPLETE, return to step 5 and rechecked
8. Clear the DTC with the HDS.
9. Select LINEAR SOL TEST in MISCELLANEOUS TEST MENU, then carry out LINEAR SOL A TEST in LINEAR SOL TEST MENU with the HDS.
Is the system okay?
YES-Intermittent failure, the system is OK at this time.
NO-Follow instructions indicated on the HDS by the tester result. Go to step 10 if any part was replaced.
10. Clear the DTC with the HDS.
11. Test-drive the vehicle in the D position in all five gears at speeds over 12 mph (20 km/h) for more than 20 seconds, then slow down to a stop.
12. Retest-drive the vehicle in the D position in all five gears at speeds over 12 mph (20 km/h) for more than 20 seconds, then slow down to a stop.
13. Check the OBD STATUS in DTCs MENU for a pass/fail test of code P0746.
Did the result indicate a pass?
YES-The problem has been corrected.
NO-Return to step 1 and recheck.

I would check the wiring to the solenoid first if you have a scan tool that can trigger it, that would be easier, but it can be done with just a test light and back probing the connector. If you take a test light connected to battery positive and unplug solenoid A then touch the test probe to pin 2 in the connector, that is the ground, and the light should light. Now for the harder test, Plug the connector back in then connect the test light to a good ground and use a needle to probe from the outside into the rear of the red wire connection. Now perform the driving test while watching the light. When the transmission shifts that solenoid, the light should come on. That would show that it has control. It sets the code if the solenoid doesn't respond when controlled. Erase the code prior to testing. You can also use a test light connected to battery positive and a wire to ground, unplug the connector and touch the ground wire to one terminal and the powered test light to the other. The solenoid should trigger and click if it's free.