Dear OP
I am so sorry you are in this situation - I have been too and it feels like the world has caved in and everything you assumed about your relationship, your family and your future has collapsed before your eyes. My DC were 7 and 5 as well - so little and so deserving of comfort and security.
(I really, really wish posters on here would show some compassion and stop throwing mud at OP and other posters about how the 7 year old knew or sensed something was wrong. It cannot be helped. Stop judging and leave OP alone - it's happened and OPs world has collapsed).
My discovery happened behind closed doors but somehow at some point my 7 yr old overheard something. It was horrible for them and later for the 5 year old too - because it isn't about one night it's about a period of time and even if OP your child didn't hear now they will at sone point realise and feel pain.
I'm not presuming what will happen to you. But I'm glad your H has left for now. I know I couldn't bear to be near my XH and I kicked him out straightaway. Then I consulted a divorce lawyer so I could understand all the implications and where I stood and then we went to counselling for a few months to decide our future. Well I decided our future.
But my circumstances were different. XH had an affair for 10 months and then ended it. But when I found out he'd just picked up another woman and started flirty texting with her. It all started to unravel..... and I found out it all. His first response was denial, then disbelief that I'd kicked him out as if he had no appreciation of the risk he'd taken with our relationship and lives. And when we went for counselling he carried on lying and minimising and that's what really did it for me. I lost any belief in his integrity and he was no longer the man I thought I'd married.
A few thoughts - these are early days and you will be struggling - switching between anger, pain and disbelief. You will feel desperate for your children - it will be hard to hold it together but hold them close and love them. Caring for them is what will help you survive.
Next try and be very kind to yourself. Get in touch with people who are really kind and supportive and who are unquestioningly there for you. Sleep when you can, accept offers of help, try to get a bit of fresh air but no worries if you feel like you can't do anything. Try to eat a little when you can stomach it - avoid alcohol it will make you even more exhausted.
Don't be shocked that you want know everything - it will drive you insane not knowing because only him and her know what's happened to your marriage - that's part of the betrayal.
Contact the OW if you want. Of course it's better to manage your communications - at least for your pride - but anything you do right now is completely understandable. I wrote to the OW and told her what I thought of her and then suggested I would be popping in to see her at her place of work. I had no intention of doing so but I liked the thought she was looking over her shoulder. But in the end that's a distraction.
Finally please know that whatever happens you will survive this, you deserve so much better. One day you will will wake up and it won't be the first thing that punches you in the stomach. Right now, it hurts. Let it out, cry yourself a river. It will help you recover. Big hugs OP xxx