Here is a friendly tip from a recent experience with a similar task.
In order to remove the door lock barrel, as you have already learned, you need to remove the retainer clip.
Reinstallation is not the reverse of disassembly. Put the clip back in first, which is relatively easy then put the lock barrel back in. Just push it back in. The lock barrel is designed to be put back in with the clip in place. If you do it the other way around (which many seem to do), it is an unnecessarily difficult task.