Brent, I have the feeling that when you were a little boy, you drove your mom crazy by asking “Why” all the time? Yes, it is complicated how you define ministerial exception. I find myself driven to the lawyer’s answer of “It depends,” just as I expect your mom sometimes said, “Because.”
You ask how to define a minister. Why does this matter? Most importantly, for conduct and character standards, and to some extent for tax reasons. Generally, you do not have to be accredited or ordained to be a minister. For instance, youth ministers and music ministers have both been found to be ministers, even though they are not ordained. Some denominations don’t even use ordination or accreditation. The general rule is that the religious organization carries out its religious calling by choosing ministers, and to some extent, that is its choice and the courts will probably defer to that. But of course, it’s not that simple, because it is defined partly by constitutional law and partly by the laws of various states defining ministers or clergy.
Could you personally be a minister because you are employed by a 501(c)(3)? Probably not, because your organization is not a church specifically or very much like one. Some mission organizations are considered churches, or they are similar enough as a religious organization that similar standards would apply. (Take note, Brent, this is not legal advice, because I don’t know that much about your structure and situation!)
Now on to your missionary wife question. For tax purposes, it may not matter, because she may not get a salary anyway. I know I didn’t, when we were on the field, since half of not-very-much would have been practically nothing anyway. For the purposes of defining roles, responsibilities, and standards, it may matter a lot how your missionary wife is defined. I liked one mission’s job description for a young mom that said her primary ministry was to the children (given how many MKs over the years have felt neglected for the work)—they obviously considered her a minister. A woman could be a minister even if the organization does not ordain women. Or the religious requirements for a male minister could include conduct standards within the family. You want to be pretty careful if you differentiate between married and single women, or between women and men, in working all this out. You can’t just ignore gender discrimination issues.
The team leader? Just an even-more-busy minister and professional, who has some administrative leadership tasks. This is all very broad-brush and is not legal advice. But an organization working through this probably would need legal advice!
Disclaimer: not official legal or psychological advice or opinion