I have a very awesome friend who did in home childcare for years. The parents of one of the kids she watched separated and then divorced. It was super messy. Not the divorce as much as the relationship. They were ugly about each other and angry with each other and there was a lot of game playing, lying, blaming and passive agressive behavior. The little boy was miserable and, to be honest, so was my friend.
I understand, in home childcare is a little different, it's more intimate and you get to know the parents more personally. What I will say is that, this is when all of that backfires. I think you should look at both of them and honestly say,
"You talk to me and your spouse knows, your spouse talks to me and you know. Either one of you could supoena me and I would have to testify in the divorce, custody, and child support proceedings. No matter who called me in, I would have to answer both attorneys questions honestly and I wouldn't lie for either one of you. So, in the best interest of all of us, please, oh please, oh pretty, pretty, please, don't talk to me about this anymore."
You have to be the impartial person for this child.
As to these two, both of their priorities sound so far out of whack. If they are not divorced they need to cut out the dating until they are or at least have the papers filed and a date set. They need to be focussing on their children and working WITH each other in regards to the raising of their children. You, of all people, do not need to be the middle man. They need to grow up, put on their big boy and girl pants, and get to the business of taking care of those kids.