In my experience, in MN, a judge would not take a private investigator's report as evidence in court. In our case, the ONLY recommendation that the judge considered was a custody evaluation done by a person that the judge himself appointed to do it. We wasted a lot of money paying for a private custody evaluation and the judge refused to even read it.
It is likely that the fact that their father would be away from home for 2/3 of the time would affect your ability to get more parenting time, or a change in custody. But in the end it is up to the judge and the laws of your state.
My stepkids lived in a horrible area (they watched America's Most Wanted being filmed on their block, for example) and were both neglected and abused. We could not get the court to allow them to live with us until they were 14 & 16 and made the decision themselves. We spent tens of thousands of dollars in legal fees to lawyers, custody evaluators, and mediators with no luck. Our 16 year-old had to sneak away while her mother was at work and drive herself from Chicago to Minneapolis before she was able to live with us!! The 14 year-old had to call us WHILE he was being beaten so that we could call the Chicago cops to go to their house while we listened on the phone.
Sorry to share such a negative story, but it worked out in the end and after extensive counseling as teenagers, I am now stepmom to two quite well-adjusted adults! Be there for your stepdaughter in every way you can. Sometimes the legal fight is not worth the drama, and it's better to be the one stable influence to a child, even part-time, that can make a huge difference.