Forgive me, I didn't read any of the responses before posting this as I didn't have much time. I'll check back later and review. Just wanted to respond to this from the OP:
While I am sure you love and adore your kids, I completely sympathize with your not wanting the burden of caring for kids that young at this time in your life. You need to communicate to her than YOUR KIDS WILL SENSE that they are overwhelmingly NOT WANTED by you, and it will cause them psychological and socialization harms which neither you nor your ex would want for them.
I was raised by a father who wanted children, just not the burden of actually interacting with them. Well, me, anyway. I don't know about the others. I was the last in the line and could sense that he didn't want me bothering him. It affected my relationships with men VERY negatively, and still does to some extent. I've always believed men couldn't love women because my own father didn't show me affection.
So yeah, I'm with the playboy on this one, sad as I am to admit it. I truly wish every child could be born wanted by both parents, but that just isn't the case. My own kids haven't had a father for most of their lives because I couldn't find a man who was emotionally strong enough to love me and raise them. I've had them 100% of the time for 13 years now.
Would you believe it always shocks me when I meet a man who not only loves his wife, but his kids, too?
I can't even wrap my brain around it.