Was Leia loyal to jabba the Hutt and If so how did he subdue her?

It was unlikely that she was "loyal to Jabba," per se. He kept her with a collar around her neck with a chain, and had to repeatedly pull on it, choking her painfully, in order to bring her half-naked body closer to himself. However, on the Sail Barge, she is standing by the window looking out at her friends on their way to their execution when Jabba pulls her chain. Subsequently, she is clearly seen jumping up on his throne and pressing herself (lower body first) against his belly, suggesting that there was at least some form of responsibility she had taken to him during her time as his slave. Loyalty, however, was a ways off, as his statement "Soon you will learn to appreciate me" would indicate.