You fire TKM for the PR mess she created and the storm she has been unable to manage. The lack of understanding from her is beyond ridiculous.
You bring in a new AD and keep Rice for another year.
If Rice fails again you can let him go and have the AD bring in his "own" guy to coach and use that as another reason for the firing.
Everyone will be happy short term, TKM gone from the mess, Rice stays. Long term if Rice doesn't work this year he's gone and we start over new coach new AD. The end.
You bring in a new AD and keep Rice for another year.
If Rice fails again you can let him go and have the AD bring in his "own" guy to coach and use that as another reason for the firing.
Everyone will be happy short term, TKM gone from the mess, Rice stays. Long term if Rice doesn't work this year he's gone and we start over new coach new AD. The end.