I remember being where you are...when your child has not done it yet you can't imagine that they ever will, whether it's falling to sleep alone, potty learning or whatever. My pediatrician kept bugging me because one kid was a late walker....he acted like he would never learn to walk, but he did. I thought my daughter would NEVER wean herself but she did....when SHE was ready not when I was.....although I do feel nursing is more negotiable as the child gets older, depending on their personality.
I assure you though, this Western/American idea that loving our children to sleep, that "parenting to sleep" as Dr. Sears calls it, is indulging them or spoiling them......It's Just Not True. It's a myth of our culture. They DO outgrow it when they are ready. My dd sometimes fell asleep on her own starting at 2. Every child is different.
Personally I found lying down with a child (or two sometimes) gave me much more sleep than the times I loved them until they were sound asleep and THEN put them down. But that's a personal choice.
Take the time to heal from your marriage before you move on with someone else. Make a list of all the qualities you would like in a new partner and then work on growing that way yourself. ~mandib50