Honestly, I am no expert on this field. I could imagine that without a third part like a therapist it could be tricky to get the settings clear, it could prevent disagreement about the agreement. And you have children together, so it a lot to think about.
So it could be something to consider.
BTW, there is an article about therapeutic separation on the Staying board, you may find it here:
Therapeutic Separation. Perhaps this can give you some inputs too.