Please make sure that if the control is switched to appropriate letter, make sure that the same letter is selected on the locomotive.

For example, if you are using "C" for one control unit, use the same letter "C" for one locomotive. Alternately, switch to the other letter "D" for other locomotive.

I believe both the locomotives may have the same letter and this may have confused the wireless controller on both locomotives........I guess!!!

I am not an expert on these models, but I have dealt with radio controlled toys, wireless broadcasting systems (radio and infra red). I agree that the problem may be linked to overlap of signals between the two units. In the video, both trains were working properly. Other than changing the batteries, did you change any other settings since then? Some remote controls (TV) require that when batteries are removed, that the remote be paired with the receiver once new batteries are installed.

Each controller has an option for A or B. I believe that each locomotive also has the same A or B switch. Make sure that one controller and locomotive are set to A and the other controller and locomotive are set to B.
The first thing that I would do is to focus on one controller and locomotive. It is probably easier to test using just one rather than trying to repair both at the same time. Can you identify which controller came with which set? They are likely fully interchangeable, so this may not be too important.

Take the locomotive that you want to use. remove the battery pack as stated in the instructions, ensure that all four batteries have been properly installed. If you have a volt meter, test the outputs (the back (-) of the last battery and the front (+) of the first one to check to see if you are getting between 5.4 and 6V DC.
Do the same to the controller. Make sure that the two batteries are properly installed and that the voltage output is between 2.6 and 3V DC.
Make sure that both controller and locomotive are set to the same channel (A or B as you choose).
Depress the main switch on the locomotive and see whether it responds to the controller. I am not certain if you have to also depress the "stop" button to activate the controller. It may be only an emergency stop or it may be a Start/Stop button.

If it does not work, (turn off the locomotive), remove the batteries from the controller, take the second controller, install the batteries and set it to match the channel of the locomotive and test to see whether it works.

Were the children playing with the innards (battery compartments)? Make sure that the contacts are making contact with the batteries, that they are not dirty. You can clean them with a toothpick and rubbing alcohol. Do this carefully as I do not know how the plastic might react to the alcohol.
Did you have any problems with battery leakage. If the contacts become corroded, it can sometime prevent power from reaching the device.
The remote controllers consist of a PC board with buttons mounted that is installed inside the plastic shell. The controller can be damaged if dropped and sometimes buttons will cease to respond on their own. I have had this problem with several remotes for audio/TV and on one of my 6021 digital controllers. The PC board is usually covered by a plastic membrane that has the button tops moulded into it, or is a flat surface over which the buttons sit.

If you cannot get the sets to work, you should check with your local dealer or with another modeller in your area to see if they have a controller that you can test your locomotive with. This will help you determine if the problem is with the locomotive or with the controller.

It may not be a bad idea to have a spare controller that you can safely keep to replace one of the other ones if it becomes damaged (if dropped, moistened or otherwise damaged).

Regards

Mike C