Typically one will spell out the division of assets in a separation agreement. That can be done at any time. You can even write up such an agreement when you are at the peak of marital bliss if you really wanted, although it might be unusual.

They seem to be happy to maintain a relationship, even if just for the kids, so there is no social division.

Divorce doesn't really mean much – other than allowing you to get married again, I suppose. It's a pretty handwavvy concept to begin with.