editing a sqllite database from the command line within an iPad
I would like to bring up that you do not need to jailbreak your iPad in order to pull this off.  You may still want it jailbroken for other reasons, but that is up to you. 

First download iSSH from the Apple store.  It is $10, but it is worth every penny.  That will allow you to securely log into the server that already stores the SQLite database.  You said that you are currently using SCP to access the database, so SSH is already set up for you on the server side.  Just log into the server with the same credentials you use to SCP to/from it. 

If you are SSHing in, you aren't going to have access to a GUI program to alter the SQLite database.  You will have to do it using the SQLite command line tool "sqlite3".  This really is easier than you think it is, and I personally feel that using the command line interface for SQL databases really help you understand them much better.