Hrm I'm not completly sure what you want. What I gather is

You have DB1, that is always current, and you take weekly backups. You said they are not logical, but exports. Those are the same thing :) Is it a cold backup, hot backup or an export?

You also have DB2, which from your example you want the data as of one year ago for the same week. I assume the data changes or you could just query off DB2 (or some copy) for the year old data.

Is DB2 always a year behind DB1 or do the reporting requirements change frequently? Is there a reason DB2 can't be a clone of DB1 more geared twoards data warehousing and reporting and kept current, or does the data have to be from the old backups?

Assuming you need just the data from a specific weekly backup,

If your backups are cold backups of DB1, and you can take down the database to restore it weekly, your easiest bet is just to re-open DB2 from whatever DB1 backup you need, just put the files in place (datafiles, control files, etc) and open it up.

If your backups are hot backups you can follow a similar procedure but might need to either use archived logs or fake recovery. Your probably better off with a cold backup assuming it's possible.

If your backups are exports, you should just be able to create a fresh DB2 and import whatever full backup you need.

If you can keep each week or so of data in it's own tablespace you could use the transportable tablespaces but not sure if that's feasable, it would depend on your application.