Hello. Thank you for coming to JustAnswer. I am Thoreau and I am sending this answer to you only a few minutes after you asked your question.
You are correct that the primary issue is the child's best interests. There's no one way to show that a child's best interest are served by granting one parent greater custodial rights than the other and there's no way to really gauge how easy or difficult it will be. Unfortunately, the law just isn't as clear as we might like in that regard and there are no "silver bullets" to achieve a favorable outcome. That said, your girlfriend could show that the child's best interests are served by her request using anything relevant to the child's well-being. For instance, if the other parent has a criminal history, abuses alcohol or other substances, etc. those things can be very, very serious in the judge's eyes. Other factors are also relevant, and issues related to schooling, social matters, and family ties can also be important. However, it's also worth noting that the judge may not approve of her cohabitation
with a significant other (some judges see that as a moral issue and others may see it as confusing for a child), and that could adversely affect her. Ultimately, the consideration involves the totality of the circumstances and the court considers everything that's relevant to the child's well-being. Ultimately, the custodial parent
will be awarded child support according to state guidelines. You can get a rough estimate as to what support might be ordered by using a child support calculator like this one: http://www.alllaw.com/calculators/childsupport/florida/.
I wish you and your family all the best. Please remember that my job here is to provide accurate information about the law. Providing bad news is the hardest part of doing my job but it's a big part of doing my job well. If you feel that the law is wrong or unfair, I'd strongly encourage you to contact your legislators, as they are the only ones who can change it.