There are going to be some really tough days where you feel like your not doing anything right and wondering if you should be the one doing it at all - believe me it will get better.
My husband walked out on myself and our two children on xmas day - sounds bad but by that point it was a relief, after putting us all through months of emotional abuse which I look back on now as him trying to get me to end the relationship rather than face up to his own feelings and do it himself, he later admitted to having an affair since September. Anyway...it was the best thing but that still doesn't mean its not going to hurt like hell. I had days where I struggled to carry on with my routine, I felt like I was zombie-ing through it but youll do it because you love your kids and then youll go to bed once then are asleep and let it all out. That's ok - you need to have an emotional purge.
I would say is do something to change your environment even if its just some new curtains for the house, if you have to remain in what was your family home like I do then this is something that sounds silly but will really help.
Get to a solicitor and talk about your options for me divorce was the only real option as I need the financial stability from him (We agreed that I would leave my career to look after the kids and then I started university in order to retrain for another career - nearly finished now)and there was no guarantee that without a financial order he would pay up.
support network you need to build one around you, whether it be a group like gingerbread or just a fellow single parent or friend who understands what your going through and is happy to let you bend their ear every so often. Happy to be one of those, if you need it. I started going to a counsellor which was every week and is now once a month which is a safe space for me to vent my emotions rather than blast it all over social media - its so easy to do but definitely don't do that lol something like that will also help you not fall into the anger zone and stay there because if you don't know already separating from a long term partner is a loss comparable death, its the death of your relationship and you will go through the stages of grief.
contact give it a rest period even if its just a few more days but find out from the ex what the expectations are for contact if there are any. For my two children there is none from their dad, I spent a long time trying to convince him to see them but all I did was stress myself out so don't go down that road but let the ex know the door is open to them but make sure they know the conditions that protect the welfare of your children.
You should also be able to get support for your children, my kids school was brilliant and they have organised play therapy for my children if I feel they need it. They did and sometimes still do, and yours no doubt too, ask about their dad, why he left them, does he love them etc and it can be overwhelming to answer these so they might need someone who can help them through their emotions too.
I hope you have been feeling better since you posted. You'll get there. x