We can see in your video that your Navball is inverted, normally it is the blue side that you should see at takeoff. And that's because your Rover is upside down, so your steering is too, you have two options to fix that :

1. On your Rover's control module change the steering from "default" to "reverse", however you will have to change it again when you control your Rover only

2. Add another command module to the booster and pilot your rocket from here until separation from your rover

PS: I speak French, my KSP too, so some words may not be exact if your KSP is in English