1)
Why did they specifically mention their children and animals?
1.
Ramban: They mentioned animals, because animals need a lot of water; and children, so that Moshe should Daven quickly, since children cannot survive at all without water. 1
2.
Mechilta: The Torah is comparing a person's animal to himself, inasmuch as it constitutes his livelihood - 'Someone who travels without his animal is in trouble!' 2
1
See Ramban, who briefly discusses (here and in 17:5 [DH 'v'ha'Sela']) the second incident where they had no water (in Bamidbar 20:11).
2
See Torah Temimah, note 3.
