Hello B.. I have an 8 month old son and I had similiar fears as you. Women in my family have very long, hard births. They all told me "it's natural, it's what a woman is created to be able to do." Yet my mother's bladder is falling and my sister at 36 is practically incontenant (sp?). Now I can't say anything about your specific fear however I will tell you, I really did not want to have a pushing birth. I heard enough about tearing, bleeding, not being able to sit well, etc etc, to make me very fearful. Many mom's I know said the healing process from a vaginal birth was harder to deal with than the actual birth! And now I know you can force an anurism. No thanks.
Besides for that, I had lower back problems that got me out of work a month early for my maternity leave. I read that Dr's are either really into giving a c-section or they're not. I thankfully worked with a group of doctors that are very liberal on this topic. They knew about my back issues which can lead to a long labor but as soon as I got into the long, hard births that run in my family, they were pretty apt to leaving it up to me as to what I wanted to do. Personally, I would really advise you to just tell your Dr something more female medically related rather than your father and an anurism. I honestly feel your concern is waranted but you have to make them believe that something with the BIRTH could effect you or your child. If you think about it, there's probably something in your or your family's medical past that could raise concern.
And I will tell you, I will never have a vaginal birth after having my son with a c. So many people thought I was nuts because I wanted the c-section but I had such a great experience. There were no surprises, I knew when I was going to have him, I didn't have to scream in pain for 18 hours, I didn't have to worry about my water breaking...I packed my bag, went to the hospital at 5 AM and very peacfully at 7:51 my son came into this world. The incision isn't cute but it's not a big deal; mine healed very quickly and I was at home walking stairs and picking up my son after 4 days. The way they used to do a c-secion a long time ago was very debilitation but it's really, honestly not anymore. They don't cut the muscle, they spread it so you have control over your stomach again much sooner than long ago. Now mind you, I'm not telling you that you will jump off the table and will be doing lunges any time soon but you will heal very quick and I rather have stickes on my abdomen and not "down there."
Some final food for thought is that I compared the number of women I talked to who had hard vaginal births vs. those who had hard c-sectio births and the number was x4. A very large portion of vag births said they were induced, they pushed for hours or something else went wrong that inevitably led them to having a c-section anyway. I had a very good experience with mine and I really do encourage you to speak to your doctors but like I said, I would give them female related medical reasons. Don't forget that baby doctors hear it all and they have to use their best judgement in making a decision about this so plead them your best case and hope for the best.
I wish you a lot of luck!!! You will be thrilled no matter what the situation turns out to be. Once you see that little face, you'll forget all about the birth. It's an amazing experience and I hope all the best for you and your new family! You are more than welcome to ask me anything else you'd like.
With best regards,
S.