Something else to look into (bakunin please verify still possible - I do not have a PowerHA/SystemMirror config to review) would be to remove the mount/unmount from the start/stop scripts.
Instead, make the mounts part of the resource group - and the resource group makes sure the mounts are active before calling the start script and the unmounts are called after the stop script.
Or, create a resource group parent-child relationship (e.g., you want the NFS mounts active across the cluster, but the application is active on only one node.) With this setup - to activate the current application (call this appA) it would only start if the NFS mounts are already active (appMounts).
As Bakunin says - PowerHA/SystemMirror can make things worse if you do not understand it. If you need short term assistance I would recommend contacting IBM Lab Services for a healthcheck and/or workshop (on-site)
Or, contact an education center for SystemMirror/PowerHA class schedule and prices - and go with at least two admins (or you become the SPOF - single point of failure)