Getting him to talk can be difficult, many men don't open up well. I stopped talking to my wife because evry time I did it led to an argument. If I was upset, and wanted to explain why, she would become angry at me because I was upset. She became very defensive and whatever was wrong would ultimately become my fault. A good counselor can help, if you can get him to one.
As far as the lunch with the lady friend, if he was keeping it from you, there is a good chance he is at least thinking about something more happening there. A man with a 6 month old child in the house may neglected and want female company, even though it might just be someone to talk to.
I don't think you were wrong to stand your ground, but maybe a little hasty to file for divorce. Give it a little time, and muster everything you can to be calm in his presence. (not cold, but calm). Save your emotions for when he is away