Rear end upgrade

I just bought the vehicle and I am hearing/feeling a light shudder when just taking off while turning but not when going straight. I hear it has to do with the clutch plates wearing out on the inside of the rear end. If I installed an Eaton Detroit Trutrac posi kit would this kit stop that from happening? And the goal is to have the added positive traction feature. I’m a diehard DIY guy. So would you happen to have a good how-to for installing this product? Or a good online repair manual? What’s involved and how should I go about this. Local 4 Wheel Parts store wants to charge $500.00 to $600.00 for labor and part(s) together. With them is over $1,100.00. Not looking to pay that. I have floor jacks and jack stands and most other tools. Thank you!