The traverse has suspension components in the rear on each side that are attached using rubber bushings. When these bushings begin to wear the car will shift to one side or the other. When travelling straight down the road the smallest steering motion will cause the momentum of the car to shift directions, effectively pulling the car to one side or the other. As the driver attempts to counter steer to correct this shift, the car will shift back the other direction. Because the bushings arent tight this back and forth motion causes the wobble you are describing. I beleive there is three components on each side that are rubber mounted that join the cars chassis to the wheel assembly, and by jacking the vehicle up and using a prybar, you can usually see the sloppy movement easily.
https://www.engine-codes.com/p1621.html
This site has several possibilities including low voltage to the electrical system causing various drivability problems.
take the air temp sensor off. and leave in warm house. till at your homes warm temp then go out and install the sensor.and start engine. if it starts this is your problem.
DTC P0717: Input Speed Sensor Circuit Low Voltage
If you don't know anything about automotive electronic's , sensor electrical circuit's ,your best bet would be to take your vehicle to a qualified repair shop.
Finding a wiring diagram ,reading how this sensor work's an testing the electrical circuit using a DVOM - digital volt ohm meter , going by a factory service repair manual .
Diagnostic Fault Information
Circuit/System Description
The input speed sensor (ISS) is a hall-effect type sensor. The sensor faces the 1-2-3-4 and 3-5-R clutch housing machined teeth surface. The sensor receives 8.3-9.3 volts on the input/output speed sensor (ISS/OSS) supply voltage circuit from the transmission control module (TCM). As the 1-2-3-4 and 3-5-R clutch housing rotates, the sensor produces a signal frequency based on the machined surface of the 1-2-3-4 and 3-5-R clutch housing. This signal is transmitted through the ISS signal circuit to the control solenoid (w/body and TCM) valve assembly. The control solenoid (w/body and TCM) valve assembly uses the ISS signal to determine line pressure, transmission shift patterns, torque converter clutch (TCC) slip speed and gear ratio.
Circuit/System Verification
Engine idling, observe the scan tool Transmission ISS parameter while varying the engine speed. The Transmission ISS parameter should change with the engine speed and not drop out.
Operate the vehicle within the Conditions for Running the DTC to verify the DTC does not reset. You may also operate the vehicle within the conditions that you observed from the Freeze Frame/Failure Records data.
Your best bet ,take it to a qualified repair shop.
Most likely is fuel filter; if it does it with a new fuel filter check fuel pressure at engine at speed it looses power--maybe the fuel pump is laying down.
OK. you had the battery disconnected. Here is what you do. Turn on the key. The security light will begin to flash. Wait (about 10 minutes) with the key in the ON position. The security light will stop flashing. TURN OFF the key. Then, turn on the key and start the car. Security system is supposed to prevent theft for a 10 minute delay. This usually discourages any thief. This will work, You just need to be patient with the 10 minutes. It seems like an hour when you wait ten minutes for that security light to stop flashing.
A flashing check engine light means that you have an engine misfire, You need to have the fault codes read with a code reader or scan tool. Many auto parts stores do this test for free (except Calif.)
Everyone always says crank sensor, but it is rarely ever the sensor. Crank the engine and look at your RPM gauge. If the gauge even moves a tiny bit, your sensor is good. You also need a fully charged battery to start your car in the cold. It seems like you are having trouble getting your vehicle started. There are 4 things you need for an engine to run. Fuel, Air, Spark, Compression. You need to test for all of these. Is there gas in tank? Can you hear the fuel pump turn on when the key is the RUN position? Is there air going in and out of the engine? If all of those check out, you'll have to get your hands dirty with the next tests. You'll need to check fuel pressure, test for spark, and check compression.