Tubal Ligation?

It would be very, very rare for the bladder to be perforated during a tubal ligation. If your doctor doesn't recommend that operation and recommends that you have an IUD inserted instead, it's probably because she's not a surgeon.

You'll be asleep under anesthesia during the operation.  A tubal ligation involves an incision low on your abdomen, between your belly button and the top of your pubic bone. Each tube is cut in two, and the two raw ends are cauterized and sealed shut. It would be very rate for the two ends to ever "grow back together" - they're left completely separate from one another and they'll never touch one another.

If you have a tubal ligation, you can consider yourself sterile afterward. 

Google post tubal ligation syndrome.

Make hubby get a vasectomy instead

I had one done when my third and last child was being born through a c-section.I made it clear well before and they must have asked me several times during the section.Simple, no problems.

Bladder perforation ? Only if it is done by someone with no medical knowledge. This is a simple Op here in the U.K.

Or, 

Persuade your partner to have a vasectomy.

Your doctor just thinks that you could change your mind about having children. Find a different doctor if you really want to have it done. You can google the risks. The IUD is not without risks and there are women that still get pregnant on them as well. If your partner also wants no more children, then have him get a vasectomy.

My friend had a tubal litigation done. No complications with surgery, but it failed, and she got pregnant again.

I've had an IUD (Mirena) for 6 years, and not had any problems whatsoever.