Why should it be a new wagon?
Radak: For Kedushah of the Aron, it should be a wagon that work was not done with it. Malbim - something that a commoner used, it should not be used for Hashem.
Malbim: It is harder to lead a new wagon. (This makes it a better test, if it was Hashgachah.)
What are Alos?
Rashi: They are nursing [cows]. Malbim - they do not normally pull loads.
Why did they want cows that never had a yoke on them?
Rashi: This was part of the test - they are not proper to pull [a wagon], and they yearn for their children. If the Aron has power that they will bring it [back to Yisrael] by themselves, you will know that [the Aron] did this [affliction] to us.
Radak, Malbim: For Kedushah of the Aron, it should be cows that work was not done with them, just like the wagon should be new.
Why will they put their children in the house?
Rashi: They yearn for their children [Malbim - and by nature, they should return to them, and surely not go to another land.