Someone else may read this later

Not a reason to write for an audience. A reason to write the thing you would still stand behind.

The situation

Written communication between separated parents is frequently retained and may be read later by an attorney, a mediator, or in some circumstances a court.

Whether any particular record is admissible anywhere is a legal question that varies by jurisdiction and by case. Nobody should tell you otherwise.

What this does not mean

It does not mean performing for a hypothetical judge. People can tell, and messages written as exhibits read as exactly that.

It also makes ordinary coordination worse, which is the thing that actually matters day to day.

What it does mean

Write what you would still stand behind in six months, when you are calmer and the specific grievance has faded.

That is a lower bar than performing and a higher bar than reacting.

Do not write for the record. Write something you would not mind being in it.

The practical version

State facts and requests. Avoid characterising the other person's motives, which is unprovable and reads badly regardless of accuracy.

Keep one subject per message. Long mixed messages produce partial replies and then arguments about what was ignored.

What consistently reads badly later

Sarcasm, which does not survive being read without tone. Anything about a new partner. Anything about money framed as a grievance rather than a question.

And volume. A pattern of many messages reads differently from the content of any one of them.

The thing that helps most

Answering the logistical question first, before anything else. It is the part the other person actually needs and the part that will look reasonable to anybody reading afterwards.