I think you may have “restart docker” listed before “daemon reload” in your handlers file.
That part of the ansible documentation is a bit misleading. It means that handlers are executed in the order they are written in the handlers file, not the order they are notified.
This is little more clear in the documentation:
Handlers always run in the order they are defined, not in the order listed in the notify-statement. This is also the case for handlers using listen.