Me Ex Wife Wants To Enroll Our Son In Her Underperforming School District Because It's Convenient [pa]

How can I best argue my point to a judge to get my son enrolled in the better school district between myself and my ex-wife? After reading the details, is this something I should get an attorney for, or can I expect to make a solid argument on my own?

My ex-wife and I live in Pennsylvania and share legal and physical custody of our 5yo son. Physical and legal custody is 50-50 with her listed as the primary parent. He spends one 7 day period with me and one 7 day period with her. We have been very amicable and flexible when it comes to adjusting our time with him when needed. He starts school this coming fall and we have not been able to come to an agreement on which school district he will be enrolled in. All of the arguments or points I bring up below have happened in writing and would be able to be presented as evidence if necessary.

I live in one of the top school districts in the state (Niche Rating A) and she lives in an average at best school district (Niche Rating C). Both schools have a 16:1 student to teacher ratio. Her living situation is also temporary. She is living in her sister's home and there is no lease agreement in place. She has stated to me that she plans on moving in with her LDR boyfriend, who she claims is moving to PA, at some point, but does not know when or what school district she will be moving in to.

She argues that my living situation is also temporary, but only in the sense that my wife and I are looking for more space as our family expands. We currently live in an apartment with a lease in place, and are house hunting within the same school district for a larger home. We already have a child in the household enrolled in school - my step-daughter, whom I'm in the process of adopting. While we will be moving in the near future, staying in our current school district is a must for us.

When we first started discussing his enrollment her first response was that getting him to school when he's with her would be inconvenient to her. We live about 30 minutes apart from each other and part of our custody agreement is that we must not move so far away as to cause unreasonable inconvenience for the other parent to exercise their right to their time with our son. My response was that it would be equally inconvenient for me if he was enrolled in her school district, and since we share physical and legal custody, that's a moot point. We should also be willing to make sacrifices when it comes to giving him the best opportunities in life. She works from home with a flexible schedule, I also have a flexible schedule, and my wife makes her own schedule. We have offered to get him to school when he's with her at our own expense, because, as I stated before, we believe as parents it's our job to make sacrifices to give our children a better life.

Finally, she argues that she is afraid that the size of my school district would negatively impact our son. My counter to that is that the student to teacher ratio is identical. Her school district has about 1,500 students and mine has about 9,500. She says her school district is "still pretty good". My school is ranked in the top 20 school districts in the state and the district she lives in is nearly dead last.

I've given her close to 6 months so far to come up with something better than "I'm not sure yet", and with the school year approaching I fear this is an issue we'll have to go to court for. At this point, I've stated that our son's education is not something I'm willing to compromise on, and that if we can't make this decision together I will be taking her to court in the beginning of February. With that in mind, given the details I've provided, is this something I should splurge on an attorney for, or can I make a solid argument on my own?

TL;DR - My ex-wife who I have 50-50 physical and legal custody with wants to enroll our son in one of the worst school districts in the state when I live in one of the best school districts in the state