Newbie- we bought a lemon! Delamination issues

A used car dealership is just trying to offload a trade-in and probably knew nothing about it, thus the easy lies. If you can't cancel the deal, before you start tearing things apart, you need to finds the leak source(s).

Typically, that would be the roof/sidewall joints and/or the window. Take off the sealing strip first, then the window and locate the extent of area that needs regluing. I suspect there are a few youtube videos showing processes.