Torn between my parents and fiancé

I have been with my guy for almost 12 years and have been engaged for the past year, also We have a 4 year old daughter. Recently I have been feeling confused about how I feel about our relationship. My dad has been venting to me about how he dislikes him and how he is disrespectful to him and my mom. And I do admit that at times he can be rude but I feel like my parents are also pinpointing everything. We currently live with my parents and brother but my fiancé wants to move out . I don't know if I should move out with him with our relationship on the rocks or just move out and see if the problem truly is our relationship and not because my parents' opinion is clouding my judgement.
What should I do?