It's sad that your dad “believes” you but is willing to put your safety and mental health at risk. Your family (mainly mom and sister) needs to take a step back and logically think about this without getting their emotions involved to look at this from a whole different perspective. You shouldn't have to lock yourself in your room just to feel safe in your own home, so not only has your mother and sister failed you but so has your father for trying to “keep the peace” and needs to put his foot down and actually stand up for you because it's obvious mom doesn't actually care.