this kind of deep emotional reaction is similar to grief - totally overwhelming, painful, devastating. But the good news is that it is a process. Anger will come at some point too.
Right now you need to focus inwards on you and your kids and to help and support each other through this. Have you stopped to think what it's like for your kids to see you screaming and wailing? what has their reaction been to him leaving? However little or big they are you need to talk to each other, listen and support one another. You can be each others' rock. separately you will be weak and vulnerable, together you and your kids will be strong and invincible.
every day get through the basis - get up, wash, clean teeth, put on clean clothes, make the bed. have breakfast. get a routine going. get outside to do some walks in the open air - it gives perspective, time to think and exercise - all of which help to stave off depression and suicidal thoughts.
mindfulness is also wonderful - start easy. get a cup of tea. hold it in your hands. how does it feel? smell it. feel the smoothness of the cup, the heat as it touches your lips, the taste and how your mouth responds. concentrate on the minutiae. sounds bonkers but it's really, really calming as it fills your head (temporarily) with the tiny stuff so the big stuff isn't in there swirling around causing mayhem. there are apps like Headspace to help too.
plan (with your kids) something to do together next Saturday and Sunday. make it different to your usual routines. Start to gently establish the new family dynamic. cook something different for dinner. research a recipe online with the kids, shop for the food, prep and cook it together. snuggle up.
the one thing you can't do is control him or what he is now doing. Take care and control of you and your kids. your path will become clear. it will. Happened to me, and 20 years on it was the best thing that ever happened to me - i'm strong, self sufficient, in love, and happy - a stark contrast to the blubbering wreck I was when he walked out with one of my friends, having already bought a house together (!).
you can do this, there is so much to gain. find your strength, hug your kids and move forward. your scary - but brilliant - new life is waiting when you are ready. Carpe Diem.