That automated password prompt gave me trouble for the longest time when doing a similar thing. If you are going to put this in a bash script, you can put the password in there somehow but it's frowned upon. Can you run the script from the remote server, so you are pulling the data instead of pushing it, if that makes sense? I think if you do it that way, you won't need a password for the machine you are reading from. You can run the script from sudo's crontab on the destination server to automate it nightly.
Your new command would simply swap the machines
Also look in the -delete option for rsync. It sounds a little scary, like you might wipe out data, but this option allows rsync to delete files in destination that were deleted at the source.
sudo rsync -r user@remote:/rtest/* /rtemp/