I had a tubal 13 years ago when I had my daughter(3rd child, I was 24 at the time). I had her by C-section so I dont know what the procedure is to do it normally. I would have love to have more children but I had so many problems it was just too risky for me. I had and still have a hard time adjusting to never having more children and it has been 13 years. But if this is something that you are sure about, then I would have all your medical records transfered to you new gyn, and then talk to him/her and explain how strongly you feel about it.
It can be difficult to get a doctor to agree since you dont have any children. In some states you have to have at least 2 children before they will tie your tubes. And in some there is also an age requirement. Many years ago in WV it was 2 kids and 21 years old.
I personally would have taken a hystorectomy instead, but they refused. My monthy cycle are horrible, I become anemic, and have had to emergency surgery due to hemmoriaging. They still wont take it all out, and I cant even have kids anymore. So you may have a challenge ahead of you. It would make it easer if there was a medical reason for it. Since your other doctor said it was the best choice for you maybe there is something he wrote down on your charts that will help the new gyn come to the same conclusion. Since you have a birth defect, will that make child birth more dangerous for you? Does this defect put your future children at risk as well?
Best of luck
