Info on change of custody in MA/getting private investigator

I need to know what kind of information my husband and I need in Massachusetts to change the current custody agreement he has with his ex. His ex moved to Florida with their 9 year old daughter and has physical custody. During her visits with us, she tells us about constant fighting between her mom and stepdad that scares her to death. She's overheard her stepdad threaten to kill her mom, he's an alcoholic who drinks currently and she talks about how scared she is when he drinks. Her mom married this guy after knowing him for only a few months. They've broken up a few times, and gotten back together. She's also witnessed him hit her mom. When she's with us, we hear about all the R rated movies she's watched in FL(The Bone Collector, for ***** sake!!!)and her mom, who we think also drinks too much, seems to spend more money on her alcohol than her daughter. One time she came for her visit with us and had an eye infection. My husband's ex explained she didn't have the money to get it cared for. Of course, all this will be denied if we go for some kind of custody. His ex is a very good liar.
Can someone help me with any information they might have on how likely it might be that we could get custody? We would like to hire a private investigator to get more info on the situation, but aren't sure how to proceed in that direction. We don't have much money and would like to get the most amount of info we can when we do hire someone. We're trying to think of which days and times might be the best as far as having the family watched. If anyone had any experience in this area, I'd appreciate the input.