What is the Chidush in "va'Ya'asu Chen"?
Malbim: They took only a little grain, for they agreed to return immediately. 1
Ha'amek Davar: They accepted the wagons and prepared themselves to come to Egypt, but not permanently, like they later said, "Ki Ein Mir'eh - we come temporarily, for there is no pasture!" (47:4). However, they were forced to remain there due to Hashem's word, as will be explained.
If Yaakov would refuse, would they go without him?! Perhaps they were sure that he would consent; and if not, they could return to Egypt to take more than grain. (PF)
Why does it say that Yosef sent wagons, "Al Pi Pharaoh"?
Rashbam 1 (to 45:19), Ohr ha'Chayim (to 45:17), Malbim: It was strictly forbidden to take wagons and animals out of Egypt without Pharaoh's permission. 2
Moshav Zekenim, citing Ri of Orleans: There was a law that no wagon may leave Egypt without the name of idolatry carved on it. Yosef needed permission to bypass this. 3
Ha'amek Davar: Yosef told his brothers that Pharaoh compelled that everyone who needs bread will come to Egypt at least for the duration of the famine, for he will not send grain. Yosef needed to tell his brothers, lest Yaakov will not want to come. His brothers did not tell Yaakov, for he himself said "I will go, and I will see him" (45:28).
Mizrachi: Also Rashi hints at this explanation.
Rashbam, Moshav Zekenim: As we find that they cut the wombs of all cows that leave Egypt (Bechoros 28b). (I.e. Yosef needed permission to send cows that were not cut. Perhaps he wanted specifically cows to draw the wagons for a better hint to Eglah Arufah! Refer to 45:27:1:1. - PF)
This is why Yaakov believed that Yosef is alive when he saw the wagons that he sent.