Welcome to the Surviving Forum! In answer to your question about what I did to deal with the absence of a significant other is I launched myself into an intensive workout program and also focused on training for local races. Working out kept me around positive people without really have to engage conversation with them. I also kept social by hosting dinner parties at my house with my friends. I did those things that I liked to do that were not always popular with my ex-wife and when I wanted to do them. Finally I made the most of the time I had when my girls were in my custody which was about 60% of the time. Eventually when I got to the point of being comfortable to start dating, I did that - which is where I am now.
As I am sure you are aware already, overtime it gets better - today you couldn't pay me to go back to the relationship I had with my ex.