So, the rule is I have to wait for Frenemy to post before I post again?
No. So long as we're both on, we can continue to post back and forth. If Frenemy signs on, since it was last her turn, then we'd have to wait for her to post, and if you're still signed in, I'd have to wait for you to post, and then Frenemy waits for me.
However, if you're not online, whoever is apart of the story line, that is online, can post in order until the person's who turn it was last signs on again.