"Va'Yira Ya'akov me'od vayetzer lo..." Considering that in Parshas VaYeitzei Hashem had promised Ya'akov a safe return to his father's home, what did he have to be afraid of? (We've discussed this before [link, link, link]and I don't want to rehash old material, but can't help mentioning the insight of the Abrabanel: Bitachon does not mean not being afraid. It means that despite being afraid, overcoming those fears and trusting in Hashem.) The Chiddushei haRI"M offers an interesting answer. He interprets, "Vayetzer lo," to mean that Ya'akov caused himself to have fear and anguish.
Ya'akov certainly could have relied on Hashem's personal promise to him that come what may, he would make it home. However, Ya'akov realized that what was on the line in this encounter with Eisav was more than his personal safety -- it was an encounter that would shape and reverberate through the history of Klal Yisrael. Though Ya'akov might have a personal guarantee from Hashem, a get out of jail free card, his children and descendants and future generations would not. Therefore, Ya'akov chose to ignore that guarantee, that personal promise, and instead model for us and all future generations how to deal with Eisav when there are no guarantees and when the danger is real. Ya'akov chose fear over safety in order to teach us how to overcome this trial.
There are two interesting ideas here. Firstly, I can't help but think that the Ch. HaRI"M mean to tell us more than just pshat in this parsha. There are lofty and exalted souls that have a special relationship with the Ribono Shel Olam -- I think that is bread and butter of the way chassidus thinks of Rebbes. And yet, rather than take advantage of the benefits of their special position, these lofty souls choose to suffer with us in order to show us how to uplift ourselves from that suffering. Like Ya'akov, they put themselves in our shoes. The same lesson can be applied in other areas as well. A teacher may know a sugya or topic inside and out, but he has to put himself in the shoes of his students who are seeing it the first time to best explain it.
Second point: Ya'akov wants to show us how to deal with Eisav without relying on the lofty level of direct hashgacha he was promised. So what does he do? -- He davens (he does other things as well, but without tefilah those other things wouldn't be enough). Apparently expecting a response to tefilah or at least to try to offer tefilah has nothing to do with special promises or direct hashgacha -- tefilah is part and parcel of normal preparation. If you have done everything practical in your power to do but haven't davended, that's not a lack of bitachon -- that's a lack of hishtadlus.