"A convert may not hold a position of Jewish communal authority." (Mishneh Torah, Hilchos Melachim 1:4)
In light of the Rambam above and the answers here, which discuss the prohibition on appointing a woman or a convert to certain positions of power, would it be permissible to make an adult female convert a leader of non-convert women, for example as the rebbetzin of a community, a mikvah lady, or the menaheles of a women's yeshiva? (May not be the best examples, but I can't think of a perfect one now.) Why or why not? Preferably, please bring sources.
Hypothesis: Since a woman is able to take the positions of power in my and any other examples, it would seem that the examples do not fall under the prohibition on women and converts taking positions of authority. Therefore, I think--though I am definitely not sure--a convert ought to be able to take these positions, too. However, there may be evidence that the prohibition on women and on converts taking positions of authority are two separate concerns, and therefore must be treated individually -- in which case it is not at all clear that converts could take power over born-Jewish women.