Shmeee, I am so sorry to hear this news.
I haven't been through it myself, but it could happen, and so cant speak from first hand experience but have had a very close friend go through it. Unfortunately his break up was fairly toxic, so he got a good solicitor and they looked after him, despite all the lies and carp his ex threw at him. He had a tough year but came through it stronger and happier and developed a close relationship with his son that couldn't be beaten I guess what I am trying to say is it will be tough as you know but you will come through stronger.
The most important thing is to look after yourself and your kids. It is the number one priority, everything else is secondary as you are the important people in this. Try to be amicable, but as I previously mentioned a good solicitor does help if needed
On a personal level I am not ashamed to admit I suffered with some severe stress, and depression a few years ago, due to a horrendous time at work, and bereavement. It felt like the worst thing in the world but it did pass. I still have my moments but I came through it stronger and wiser, and you will get through it stronger and wiser. I would recommend physical activity, I run and go to the gym and as Duffer said in a previous post, it helps, and it helps me blow away the cobwebs, dissipate anger and generally kick stress in the balls.
I hope that helps but whatever you do, and whatever happens, take care and look after yourself.