I understand what the problem is, I am trying to put some boundaries on the solution space. Since you can recover files from the Time Capsule back to the iMac the iMac obviously knows where the backup data set resides and that should be reflected in System Preferences > Time Machine and assuming you have automatic backups enabled that should be happening once an hour and no reconnection should be necessary. Neither should a reconnection be required if you trigger a manual backup. Some of my questions were an attempt to determine IF the automatic backups are still occurring.
By the same token you should never have to locate or specify the backup data set file per. se. all you need to specify is the Time Capsule (or backup drive) and Time Machine is supposed to take it from there. I had not realized previously that you were backing up to a Time Capsule. In the case of a Time Capsule the backup data sets are computername.sparsebundle which is a variant of dmg and like a dmg can be "mounted" as if it were a physical device. To see the sparseimage files on your Time Capsule in Finder requires you to connect to the Time Capsule using the password for your Airport router. (In normal use Time Machine only mounts the sparseimage while it is being accessed.)
In any case the backup data set is just files and assuming your iMac is connected to the Time Capsule should be visible in Finder on either the iMac or MacBook Pro. Since the iMac backup is not appearing in Finder and the MBP backup is, I was wondering if somehow the iMac data set managed to get encapsulated under the MBP data set which some of my questions were intended to ferret out.
