Can SQL Agent job notifications be sent to one operator for success and another for failure?
Quite frankly, I would just not use the limited operators facility through the UI and instead:


Create a step that only gets reached when the job succeeds, which e-mails person 1
Create another step that only gets reached when any step fails, which e-mails person 2


(You may need to modify multiple steps that could potentially fail, such that when they do fail, processing moves immediately to the second step above.)

You can still use operators if you like, just have the steps manually call sp_notify_operator.