I had the same scenario with you before I came in Canada. It is really tricky to prove this. But what I did is I wrote a letter of explanation about our situation that we are not living together anymore and the marriage had broken down and some more details. I also provided a notarized (sworn oath) document stating our current situation that we had been separated for many years and no chance for reconciliation (with our different addresses indicated) and gave more facts about us; that I am the sole care giver to our children,etc. I had also provided them a single parent ID (from our local government). They didnt ask for further documents and I assume I satisfied them with my provided documentation and I got a status of Legally Separated in my Visa. Hope this helps.