Rashi on Shmot 19:3 famously explains 'Bait Ya'akov' (the household of Ya'akov) to refer to the women, seeing as the 'sons of Israel', i.e. the men, were separately mentioned. This is essentially the same case as ours here in Bereishit; the reference to Ya'akov's household implies that his (surviving) wives, daughter-in laws, daughter(s-- see 37:35 ad loc.), and granddaughters.
In the same light, Bait Yosef, Yosef's household, refers to its members who have gone unmentioned: Not the women, included under Bait Ya'akov, but rather his servants and maidservants.
As for the question regarding the young children and livestock, with all probability, when Pharaoh granted permission to Yosef to leave, it was implied that he would care for those who didn't travel during Yosef's absence. After all, why would Yosef need to orchestrate a request for a few days off so carefully?
And, if one was to say that a vizier would always need to ask the ruler for permission, he still would not have to manipulate the atmosphere of his request so specifically! This holds especially true for Yosef.
After saving the Egyptian people from a catastrophic famine, after convincing Pharaoh that G-d was with him, after 26 years of faithful work, Yosef could have left without even telling Pharaoh-- and Pharaoh, if he was sensible, would've barely reprimanded him! The fact that Yosef took such precautions so as to stage the whole petition shows that something else is going on.
The request for protection/support of the children is something of qualifying importance, because the Egyptians were disgusted by shepherds (v. 34) such as the Shevatim, and so by defending the family's livestock and young ones, Pharaoh was effectively siding with Yosef-- at least culturally-- over his people. Thus, this was a huge request.