The external conflict in Breaking Dawn has to do with the Volturri who are the enforcers of vampire laws. When Irina--a cousin of the Cullens misinterprets what she sees when see observes Renesmee, the child of Edward and Bella, she goes to the Volturri claiming they created an immortal child. Immortal children were against the law because vampires are not supposed to call attention to themselves and vampire children are impossible to control. Therefore, the conflict has to do with the Volturri trying to enforce vampire law by killing Renesmee and the Cullen clan while the Cullens must prove that Renesmee is actually a half-human and half-vampire child who poses no threat to vampire culture.They gather other vampire witnesses to attest that Renesmee is no threat and to stand with them against the Volturri.
Two external conflicts would be Bella's pregnancy and the fight for her child's life. Bella is pregnant with Edward's child and this leads to her becoming drained of her own life. She is basically fighting for her life, but she wants to keep her child safe. The only people for having the baby is Rosalie and Bella and this causes issues within the family.
There are two external conflicts in Breaking Dawn.
The first one would be Bella's pregnancy. Bella's pregnancy was physically draining her of her life and she remained on the brink of death. Because of her pregnancy the Cullen family became divided for and against the baby. Of course those for having the baby were Bella and Rosalie while the rest of the family opposed it.
The second external conflict would be trying to fight for Renesmee's life and proving that she was not an immortal child to the Voltori.