I'd say when you both are comfortable with it. If you would remain friends even if you didn't work out, there is nothing wrong with hanging out and introducing your boyfriend as your "friend" and not doing any PDA like holding hands or something. They don't need to know you are together at this point if you just want to hang out together with your kids.

Once you know that your relationship is solid enough to last. You do not want to subject the kids to short term people being in their life. That makes for resentment and commitment issues when they are older. My hubby and I waited until we had been together a few months and were getting ready to move in together. My daughter already knew him and liked him--just had no idea he was with me after I divorced her dad.

I'm in the same boat. I have two kids and girlfriend has two kids. Not sure what to do either.