What's the noun for alternatingly? Here's the word you're looking for.
alternation
The reciprocal succession of (normally two) things in time or place; the act of following and being followed by turns; alternate succession, performance, or occurrence
(religion) The response of the congregation speaking alternately with the minister.
“It was a pretty gay city even then, a mecca of fun and outrageous alternativeness.”
“By means of stereotypical mentality, this very idea of alternativeness has also been extended to the pipelines.”
“Part of this strange alternativeness is that it explores primary, secondary and post-secondary, and it is aimed at student-teachers as well as teachers.”