This passage is a particular moment within a bigger Story. I'd suggest that the Story be framed like this: of all the households on earth, God chooses the household of Abraham through which to bless all households.
God, in the visible form of three persons, goes on a journey and comes to the door of Abraham's tent, to an extended family of blood- and non-blood relations, nomadic herdsmen. And there, they receive a welcome, are shown hospitality, in marked contrast to the lack of hospitality shown them by the people of the cities of the plain.
Abraham's family are incredulous to the message brought to them, of God breaking-in to their lives, even though it is not an entirely unfamiliar word. Abraham's family are creative in their disobedience, in trying to bring about their own interpretation and fulfilment of God's plan. Abraham's family get themselves into various troubles - divisions within, deceit in their relations with others. And yet. And yet, Abraham's household has welcomed God's messenger; and God works with and through that: he does not go from house to house.
From then on, we see a recurring pattern. Abraham's household (which grows through the generations) is to be a house of peace; and out from that household, certain members will be sent out to other households, to extend that peace where it is welcomed. So Joseph ends up in first Potiphar's and later Pharoah's household. So David takes for his capital the City of Peace. So God sends prophets to Abraham's household again and again, when the household forgot its calling. So Nehemiah and Esther and Daniel, among others, find themselves serving a the heart of households of Empire.
And these stories don't have Happily Ever After endings: they are stories of divine rescue, of peace triumphing over hostility, of life triumphing over death...but not for ever. These stories have a localised place and a limited scope, within a larger Story. Joseph's life-saving rule in Egypt gives way to the oppression Moses must lead the people out from under.
Within this Story, Jesus sends out disciples to search out households of peace. Within this Story, in which the household of Abraham has been divided and (repeatedly) conquered, Jesus is sent to call the household back to its own calling: to be agents of peace in the world.
As the Story continues to unfold, beyond Jesus' death and resurrection and ascension, the same pattern continues. Abraham's household - into which the Gentiles have now been incorporated - is to be a household of peace, made up of households of peace, from which some will be sent into other households of peace in order to extend peace. And, again, these stories have a place: a time and a space.
Missional church thinking tends to view Christendom as a massive defeat from which the Church, in the West, has yet to recover. Accepting that this may be polemic, I'd want to say that Christendom was a continuation of the Story of Abraham's household - an incredulous, disobedient, divided, deceitful household that nonetheless God has committed to and will not abandon; through which God has brought about triumphs of peace over hostility, albeit not yet the universal and with-out end reign of peace. Within this part of the Story, the Church has nurtured peace, blessed and been blessed by peace-makers; and has regularly needed to be called back to that calling, having forgotten it. And the story of the Church post-Christendom will be a continuation of that same Story...
What implications does this have for us?
If Luke 10 is to be taken as model for mission (and I think that it is), then:
the household - a gathered social unit that is bigger than the nuclear, let alone atomic, family - is central. This is an extended household of peace working together, strategically, to identify and encourage other households of peace. We will see this in the way Paul works too, as he imitates Jesus;
the household does this in the context of telling and participating in the Story of a God who called a particular household through which to bless every household. They are going up to Jerusalem to celebrate the Passover, to remember how after God used Abraham's household to bless the surrounding nations through Egypt, he liberated them from the subsequent captivity that prevented them from carrying on that role at another given time. We see this too - retelling the past, participating in the present - in the way Paul works, as well as in the model Jesus sets;
the household of peace in search of households of peace is not perfect: it hasn't arrived yet (pardon the pun). It is made up of squabbling siblings who vie for best place and fall into the trap of relating to other households as a household of hostility, not peace. And yet this is the household Jesus gathers and sends out. Again, we see this imperfection - by which I mean at times total contradiction - in the households of peace Paul was a father to;
the synergy of two households of peace coming together - in passing - results in a breakthrough for peace in the wider community, expressed in a variety of tangible ways. But this breakthrough is for a particular episode in the Story. Some episodes go wider and are sustained for longer than others; some are very localised; but all are a small part in the Story, the Great Drama;
'sent-ness' is not a matter of permanently being on the move (Jesus wasn't; Paul certainly wasn't) but participates in receiving others (as host) and going out as those who are dependent on the hospitality of others (as guest). One is embedded; one is transitory (and each might be a better fit for particular types of person; though all are called to both). The one is just as 'sent,' is as much an expression of the missio dei or mission of God in the world, as the other.