"is global mission work a non-negotiable for a believer? Is it something we should do because we're obligated to share the Gospel, or is it something we should do because we have been prompted by the Holy Spirit to serve in a specific part of the world? Is being "salt and light" in our day-to-day lives enough?"
My response:
I believe it is a biblical mandate that all Christians share the gospel, but not necessarily that each individual Christian must travel geographically to do so.
One of the scriptures that you quoted sums it up well..."Day after day, in the temple courts and from house to house, they never stopped teaching and proclaiming the good news that Jesus is the Christ."
We should be always proclaiming the Gospel of the Kingdom - everyday, wherever we are. In the store, at the daycare, at the bank, to our neighbors, to our friends, in joy, in sorrow, and of course, in our own homes. Yes, this is the essence of "being salt and light". But we (exhorting myself, here, too) need to be reminded that this inherently means that we actually tell people about Jesus and the Kingdom of God. Yes, we proclaim something of God's love in the way we act, how we speak to people, how we treat them...but that alone is not enough.
I do not believe that as moms we are exempt from the biblical call to "go", just because we are primarily focused on raising our own children. YES, they are our focus and first mission field, and we should not neglect our families for the sake of building up a ministry. But if we are paying any attention to the people around us as we go about our day, we will find plenty of opportunities to lift high the name of Jesus.
I think that often we interpret the call to "go and preach the Gospel" as referring exclusively or primarily to international missions because we are uncomfortable with the idea of sharing the Gospel in our own daily context. Walking as a witness for Christ daily requires that we live a life that is radically different from those who do not love God. It will require us to sometimes say things that offend people. Our nation is full of people who hate God and do not believe that they are sinful (or even that “sin” is a valid concept). The very essence of the Gospel is offensive to many. In some ways it is easier to consider the call to “go” as referring to missions trip type situations, because that would require only a limited temporal sacrifice, as opposed to a fundamental change in the way we live.
So, YES - you are mandated to preach the gospel, and to pray that the Lord of the harvest would send laborers to the field. But no, I don't think you are inherently called to travel across the world to do so.