Words such as possession, custody, and visitation were never designed for parents. They were designed for judges and lawyers.
For family friendly words consider the following:
Replace the word visit with the other home. For example, when talking to a child say, “When you are in your other home”, rather than, “When you visit your mother.” Or if you are talking to another parent, instead of saying, “When they visit their father,” say, “When they are in their other home.
Replace the word custody with parenting. For example, instead of saying, “I have custody?” say, “Our parenting arrangement is…..” This is particularly important when said in front of the children.
Replace the term your ex with your co-parent. For example, instead of saying, “My ex lives at…… ?” say,“My co parent lives at” or “Their mother/father lives at…”
In blended families, instead of the term our new family, try considering them as blended. For example, instead of saying, “Now you have two families,” say, “Now you have a blended family. Or “Now you have a larger family.
Replace the term two homes with lives with. For example, instead of saying, “He lives with me and visits his mother” say, “He lives in two homes.”
Replace my child with our child, or use their name. For example, instead of saying, “my child goes to the public school?” say, “Our child goes to the public school.” While you are no longer a couple your child is still a part of both of you.