Ahhh well done... We're getting closer!
The getTime is now showing a string of time. It's not filtering though, if I use -7 or +7 and play with the publishedon dates it will show days outside the 7 days. Ideally I need it to show resources that will be unpublished in the next 7 days because this will work as a "What's on this Week" events widget.
This is the call I've been using with the 'publishedon' just to try and get your example to work.
[[getResources? &parents=`14` &tpl=`ThisWeekTpl` &includeTVs=`1` &limit=`5` &where=`{"publishedon:<=":"[[!getTime? &from=`-7 days`]]"}`]]
This is the call I want to end up with for a "What's on this Week" widget:
[[getResources? &parents=`14` &tpl=`ThisWeekTpl` &includeTVs=`1` &limit=`5` &where=`{"unpub_date:<=":"[[!getTime? &from=`+7 days`]]"}`]]
Many thanks again for your help so far