I am so sorry OP - what a cruel and cowardly way to exit.
You are stronger and more capable than you realise. I PROMISE you that.
In order:
Arrange some leave from work. Sick leave/unpaid leave/compassionate grounds - whatever it takes. Assume it's half term for your DC this week...?
Give yourself a day or two of nothing - just disbelief and crying.
Call on ANY support you can. I know you say its limited - but is there anyone you can talk to? If not, use us! :)
Then look at yourself in the mirror. Look at your children and think about the life you all deserve and get fighting.
Get yourself a lawyer
Speak to citizens advice or use the entitled to website to ensure you are getting the financial support you are due
The hardest part will be navigating your grief (which is how it will feel for a few weeks) around the DC. You should not have to protect his reputation with them, but equally you would hope that in the future, they can have a relationship with their father. I would suggest you are honest but spare - he has decided he wants to leave. I am shocked and upset so bear with me. But we will all be okay in the end.
I am so so sorry
What a cunt
Almost certainly an OW and he will also almost certainly come crawling back at one point (quite possibly, only to dissappear again). I would say that emotionally, your priority is to get to a place of anger and outrage at this coward and ensure you are not going to crumble if he comes knocking. You deserve so much and there are definitely better days ahead. Especially as you have had your DC quite you - you have so much time to live an amazing life - don't stress that bit x