As grebneke comments, do not store the command and then execute it.
What you can do is to execute it but firstly print it: Bash: Print each command before executing?
priorday=$(date --date yesterday +"%Y-%m-%d")
outputfile="/home/CCHCS/da14/$priorday""_PROD_message_processing_times.txt"
set -o xtrace # <-- set printing mode "on"
grep 'Processed inbound' /home/rules/care/logs/RootLog* | cut -f5,6,12,16,18 -d\" \" | grep '^"$priorday"' | sed 's/\,/\./' | sed 's/ /\t/g' | sed -r 's/([0-9]+\-[0-9]+\-[0-9]+)\t/\1 /' | sed 's/ / /g' | sort >$outputfile"
set +o xtrace # <-- revert to normal