Hi Eeyote No More,
I’m not aware of any research papers on this, but my suggestion is to focus in on the children’s needs, making a list. You know your abuser and his failures better than anyone.
For example, safety, warmth, proper sleep, space and quiet time to study, proximity to friends, your ex having appropriate friendships and acquaintance and visitors to the house, routine, etc.
How would the 50/50 affect that could be your focus. Less space to study, for example, more travel time, less routine, safety and health concerns…
For example, my ex chose to move out in the sticks- more midweek travel time for my son, interrupting his school week. Trouble with transport, interruption of study, being far from friendship group, my ex inviting inappropriate people into his home and forcing my son to go to late night events mid-week…the list goes on! Never mind his games and abuse. Physical examples and details are what they want- nigbour opinion, unfortunately.
Looking up the rights of children may help you to express your concerns.