It is possible to have a co-parenting live-in relationship. It takes a lot of negotiation and communication, but there's no reason things have to end completely.
It's also worth both of you visiting whether "sex" is an essential part of "love." After so much time together, why does ending the sexual component of your relationship have to end the emotional component?
There's actually a section about this in Opening Up
, it's worth acquiring that book and reading it. You could maintain a loving, emotional marriage, but meet your sexual needs elsewhere.
Honestly, anything is possible if you're committed to it. The important thing here is for neither of you to harbour resentment or anger about what has happened. This is just who she is. She didn't do this "to you." Not that you're implying that she did, but being clear about that will help you cope with it.
And of course, you are free to explore other sexual and emotional relationships outside the marriage. No reason you should have sit at home mourning what you've lost. You can look at this as a new opportunity in your life: you get to have a loving, stable home life in which to raise your children, as well as freedom to explore romances outside of that.