What should I do about my ex?

I just got a 3 year relationship about 2 months ago and I was a chat network on the phone thinking about maybe to start dating again. I was approached with a proposition to have a “discreet” friendship with a man who is “happily married” and has two young children. I know I should have stopped talking to him but we ended up exchanging e-mails and are keeping in touch. My ex boyfriend and are trying to work things out but we keep fighting even though we are not together and he is getting very picky about every little thing. I love him with my whole heart but I am starting to realize that there can be more people out there and maybe it wouldn’t hurt to start dating again to see how things go. Anyway what does anyone think of my situation should I pursue this “discreet friendship” and what should I do about my situation with my ex boyfriend?