I'm sorry for your pain. I'd get that meeting with the lawyer set up ASAP--having him "stop around" to see the kids is not a great idea. How old are the kids?
You may FEEL "broken" now, but trust me, you aren't broken. There is nothing wrong with you that caused any of this, and once you have healed there is nothing wrong with you that will prevent you from finding a happy, healthy relationship in the future. You're not damaged goods. This isn't your destiny--there is a happy future out there for you. It just takes some time to get there.
Many hugs. I know you have a lot on your plate, but if you could try to work in some therapy to help you process everything, it would be a great investment in your own healing.