I had a problem where I wanted to restart my server then backup my database, but how to ensure the order is executed as intended?

It seems that /usr/bin/run-parts is the script that executes the scripts that are stored in /etc/cron.daily. Inspecting the script, it simply iterates over the files in the folder so a simple way to work-out which order is simply to execute the script:

for i in cron.daily/* ; do
echo $i

which will show the order.

The trick is to prefix the files with a digit which defines the order in which the scripts will be executed.