Audi never owned Volkswagen. Volkswagen has owned Audi since 1964. What is true is that there has been an attempt of Porsche AG (the sports car company, not the capital holding) to take over VW in the late 2000s, but got switcheroo'd and instead taken over by VW.

While Audi does build some engines for VW (especially in the higher-tier sector, which arguably is more of an Audi thing to begin with), VW itself produces engines itself (to name a few, the TSI-, TDI- and TGI-series of engines).

Now, does VW build good cars? It's a hit and miss. I personally drive a New Beetle, and will probably continue to drive it for years, the thing is build like a tank and reliable to a fault. Then you have models that are ... not something I would like to drive.