Jacob used several different tactics in dealing with Esau.1 He knew his brother was far more powerful than he was. Esau had four hundred warriors. By contrast, Jacob had with him only his wives and children. At that time his oldest son was twelve. These children were to be the basis of the future Jewish people. But would they survive?
Jacob tried conciliation, sending a large gift of several different kinds of livestock to Esau. Jacob succeeded in persuading Esau to accept this gift. With this went an implicit acceptance on Esau's part of the existence of Jacob and of the fact that he was in the right when he received their father's blessing.2 At the same time, Jacob prayed to G‑d, in a beautiful prayer expressing his feelings of humility. He felt that he was not worthy of all the great benefits that G‑d had already granted him.3
He was also ready to do battle. His tactic of dividing his camp in two was part of a military strategy. Jacob was completely outnumbered, and he also hated the idea of harming others.4 Nonetheless, in order to protect his own life and the lives of his wives and children, he was ready to fight.
These are all different methods of relating to Esau, the enemies of the Jewish people through the ages. In different ways, these approaches have been used at various times in our long history to ensure our survival.
Prayer of course is a constant, which is always needed. Striking the right balance between conciliation and readiness for battle is the key to saving lives for everyone concerned. The goal is peace and safety, and Jacob's meeting with Esau provides an example of skilful negotiation which was eminently successful.
The two camps This indeed comes from Rashi: 'the other camp will escape', Rashi says: "despite him [ie despite Esau], because I will battle with him." I think the underlying assumption of Rashi is that the women and children cannot run away from the swift warriors of Esau. The only way the second camp can escape is because Jacob will do battle.
By contrast Ibn Ezra expresses your opinion. The second camp will be able to flee while Esau attacks the first camp.
Ramban, Nachmanides, gives another view: Having received earlier promises from G-d, Jacob felt that surely G-d will not allow him to be completely destroyed. Hence even if one part of his camp will be destroyed, the other must survive.
The Lubavitcher Rebbe suggests that In one camp would be the livestock and servants; this would be attacked first. In the other would be the wives and children. Jacob would battle on their behalf and would be successful (as Ramban's view). See the Rebbe's discussion in full in the Gutnick Chumash.