Have you used any of the LabVIEW debugging tools (execution highlighting, probes)? To see if your tele-op mode is running, probe the wire that goes into the case structure and see if it is ever set to "TeleOp Execute." You may also want to try execution highlighting to see what is happening, but be aware that it may slow your code to the point that the watchdog will time out (in that case, disable your watchdog timer temporarily).
It is not a good idea to open a reference to the Jaguars inside your autonomous mode, since you've already opened a reference to them in your Basic Robot Main. Instead, use the RobotDriveRef global variable to get access to the motor references. You can use the "Unbundle By Name" and "Index Array" functions to extract references to the two individual motors from the RobotDriveRef.
Try wiring the through Error In and Error out from one function to another and eventually to an indicator so that you can see if an error is occurring (for example, in your TeleOp mode, wire an indicator to the Error Out terminal of SetValue). You don't need the case structure around SetValue, just negate the value that you're reading from the button and pass it directly to SetValue. Also, using "Unbundle By Name" in place of "Unbundle" to get your joystick buttons (and other places) will make your code clearer.
You have a VI named "Servo Tracking State Machinev1.vi" which is not actually a state machine and has an icon labeled "Gimbal Control." You're calling it from two different locations: once in Basic Robot Main, and another time in Autonomous Independent. While I don't think this is causing problems, it also doesn't appear to be helping.
Try to follow left-to-right flow; for example, in Autonomous Independent, the wires leading to "left motor" and "right motor" indicators on the left side of the case structure are unexpected.
I'm not sure any of these will solve your problems, but they should help make your code more readable and easier to debug, and the debugging techniques may lead you to a solution.
