When I had just turned 10, my dad remarried... and the lady he married had a 5 year old daughter. After much counseling to get us all into shape, or somewhat so, they decided that they wanted to see about adopting us... my dad adopting my sister and her mom adopting me.
My birthmother died several months before my parents even got married, and I'd been going back and forth between both of my parents for years since they divorced when I was 3... so there really wasn't much of an issue with my adoption.
My sister's birthfather is still alive, though, and they had to have him informed of my dad's wish to adopt my sister. She had visited him off and on irregularly, and he was remarried and seemingly totally engrossed with his new wife and child. My sister wanted my dad to adopt her, and was just hoping that her birthdad wouldn't pitch a royal fit about it.
...he didn't, the jerk. He didn't seem to care whatsoever, in fact. Because of that, there was no opposition to my dad's adopting my sister, either.
I can't speak for anyone else, but I know that we've gotten along just fine developmentally... I think we were about 13 and 8 when the adoption was done. My sister even changed her middle and last names, as they'll allow you to change any part of your name when you're doing the paperwork.
I don't know how hard the process is, as I was too young to have had any part of what they went through to get all of it set up... and I'd imagine it differs from county to county and even state to state, too. I do know that it just validated all that we feel now, though... even without the adoptions, I'm sure we'd still be as much a family as we are now, but I am glad that my parents went through the trouble to do it, and I know my sister feels the same way, too.
As for your own situation, I guess you really just have to do what you think is best for the kids. If you feel that seeing a birthparent is negatively impacting them, then it might be all for the best if you looked into the adoption idea... especially if the birthparents in question seem to have no desire to be there as a responsible part of the kids' lives.
Just my thoughts.
Nikole ~ mom of NJ (10/98), TJ (10/04), and AJ (12/09)