((brokenhearted81)) < a hug
Welcome. We have all been in your situation, and those "ping-ponging" emotions you are describing are brutal. You will survive this, though, and it will get better, although I will tell you honestly this will be one of the roughest things you will go through.
Please read some of the other posts, and look at the Healing Library in the yellow box to the right.
There is always someone here to listen, sympathize, and offer their opinion and experience.
You are not nuts for wanting to work it out - most people do not chuck their marriage, especially with kids involved, unless the WS makes reconciliation impossible. Although some people do find it a dealbreaker, and that is OK too. Don't feel you need to decide this - the most important thing is to focus on your healing from this trauma right now. The rest will become clear to you when you see if you WH is working on himself.
I don't believe "once a cheater always a cheater" if the person who cheats starts to take a good look at himself, figure out what they are lacking within themselves that allowed them to commit the cowardly act of betrayal, and start working on building an authentic life.
This site was actually founded by a couple who experienced infidelity, and they put many hours and dollars into making it a healing place for many - so I would say a person is not necessarily a cheater for life if they put in the work to figure themselves out.
You really don't have to make a decision now - it is good that you and your H are communicating, and when you observe his ACTIONS, you will eventually know if you feel you can commit to a reconciliation. Right now all that matters is taking care of you and your kids right now. Are you eating? Sleeping? Getting enough water?
You are not lost, you have found us, and you are welcome to post whatever is on your mind.