Could you perhaps be a little more specific?

Restore from backup.

And, just maybe, consider getting an OS and SQL version that's slightly more modern?

No such version as Windows 2007...

The size limit in SQL Express for all versions 2008 R2 and above is 10GB. If you need a larger DB than that, you need...

Replace the secondary or break the AG and re-setup once the secondary is available again. Don't think AGs added any other options.

Is the table a heap?

Are you shrinking the database after the rebuild?

Yes, normal and documented. You need to run sp_refreshview on both. Or stop using SELECT *

Add three files to TempDB, make sure they're all the same size. If you still see the latch waits after that, add another 4 files.

Are you seeing allocation contention (PAGELATCH_UP waits on 2:1:1, 2:1:2 and/or 2:1:3)? Or IO contention (slow IOs in TempDB, PageIOLatch waits in database 2?

What edition of SQL is this?

Well, without seeing the script, the table and being able to query the data, I can't say for sure, but ideally yes.

Before you do so, make sure that there is...

You will always get a lock on the table. It should be short-lived. Make sure that your split isn't forcing data to move from one partition to another, as that...

PearlJammer1 (11/28/2014)

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The other reason for this question is that I currently only have 1 TEMPDB file and I need to increase the number to reduce TEMPDB contention - and I...

The Hidden Online schedulers are not for query processing. They're for internal stuff or reserved for the DAC or other stuff like that.

What edition of SQL is that?

It's not something to get around. It's how log backups work. When you implement log shipping, it must replace any current log backup job. Otherwise neither the log shipping nor...

If you implement log shipping, those MUST be the only log backups running against that database

Add more disk space or delete data.

Or move some of the data files to other drives if there are any.