I actually have dated a girl with
two kids. I wouldn't recommend it, even though I was never really introduced as The New Father or anything, it's just unbelievably difficult in every way. As kat says, if you do get introduced it's gonna be awkward as hell, cause fighting and so on, and will continue to be for a very long time. This isn't The Holiday. For that reason (and others) we never really pushed forward with our relationship, and it just fizzled out.
Well, my case is definitely different than yours, but no matter what, I don't recommend it. As far as a learning experience, the only thing I learned is that I am more of an jealous petty asshole than I thought I was. So I wouldn't even recommend it for that.
Jam it back in, in the dark.