Me too. I was 35 with two toddlers when my ex left suddenly. Total shock, I had no idea. Now I have remarried, and so has their dad (he also has another child). We all get along fine. DCs spend 40% of their time with him, 60% with me. It works well and they have a good relationship with us both.
My divorce actually became a major turning point for me, and I now work coaching people through their divorce.
Focus on keeping your cup full so you can look after the children. Make sure you eat and sleep. Don't stuff your emotions - let them out
and acknowledge them.
Face your fears (so find out how much mortgage you could get, how much the house is worth etc) - once you know, at least you're no longer living with uncertainty and you can look at your options. I was desperate to stay in the marital home, and did manage it, but within 2 years I had moved through choice.
Look for the upside to everything - even the darkest thing has a glimmer of good, even if you can't see it at first. I remember about 3 months after my DH left, I realised that I enjoyed not having to discuss what was for dinner, or how to handle something. I could just decide, and that felt powerful and good!
I honestly see my divorce as one of the best things that ever happened to me. You may not feel you have a choice about the divorce, but you sure as hell have a choice about how to handle it. I chose not to let mine define me. I chose not to hold onto anger, as it was damaging to me, and he didn't even know - like drinking poison and expecting someone else to die.
As for shame - no-one has ever made me feel ashamed about my divorce. No-one. That is a belief in your own mind. Instead of focusing on that, focus on all the amazing things you are doing that you can be proud of - I imagine there are loads. Talk about them instead of talking about your divorce.
Sorry, just typed all that and then realised you didn't ask for advice, only for positive stories! I can't help myself.