No, Jennifer, you're not likely to feel safe in that situation. It's one of those tragic things where you simply have to get out, leap into the unknown (terrifying) and find a new, safe home. It's up to your mom to be the one steering all of that, since, if I remember correctly, you are 14. But if your dad has been so untrustworthy, the first thing you two need to do is get a safe home of your own, and then once you're there, you will have to deal with the heartbreak that will inevitably follow, the aftermath of feeling Why didn't my husband/father treat me the way I needed to be treated? etc.
Big hugs Jennifer. You'll get through this; I'm just sorry knowing it will be very painful for you and the rest of your family.