Sorry to hear this OP. You will get through it and have a better life. Don’t waste time on the OW, he is most likely using her as his excuse to walk away from his responsibilities. Let her pick up his slack and keep him fed and watered, he will jump ship once he gets his share of the money.
Practical things, with money the priority is liquid cash. Take at least 50% out of any accounts that have easy access including the current account. Make sure other savings accounts are protected. Tell him you have done this and explain that you need it for bills but understand he has immediate financial needs as well. Offer to have a sit down to work this out in a way that works for both of you.
NB whilst it might be tempting to clear out accounts, if you rely on his income then it could be counterproductive. Moneys going to be tight for both of you and if he stops supporting the family home you could be in trouble.
If you have a mortgage speak to you lender and maybe ask to go interest only until you sort out the settlement or for fixed period. If it is in anyway possible work together in the interests of the children to make finances work in the short term. Offer mediation and make an appointment.
Check your benefit entitlements, change council tax to single person, cancel sky sports, and so on. Start listing your assets and then evidencing them or documenting them. Think of the best person to recommend a good local solicitor who has good experience of the local courts and who specialises in divorce.
Get real life support from people who have you and the children’s best interests at heart. Go for friends and family who will give you positive emotional support and practical help. Because you have children it’s not a good idea to feed the bitterness and acrimony too much. At the end of the day he will be in their lives and your life for a long time. Plus it really doesn’t help. You are better than that and you are better than him.
I suggest you tell the children together and that you agree what you both want to tell them. They don’t need to be stuck in a war or have the local community gossiping about the situation, so imo discretion with them and others is a good thing.