it appears that the chart relies on the found set sort order.
That would depend on the data source options you choose for the chart. You can also chart data from a related table and then the current layout's sort order has no effect on what you get in the chart. (But some charting options have to be based on the local found set to get what you want.)
To do what you want, you could use the OnTabSwitch script trigger along with get ( TriggerTargetPanel ) (FileMaker 13) or Get ( TriggerTargetTabPanel) (FileMaker 12) to identify which tab panel has been clicked. You'll want to look these up in Help.
But if the only difference in your charts is the sort order of your data, you don't need multiple tab panels with multiple charts. You can have just one chart and click a button or select from a drop down to resort the records to produce different charts.
I think I like your last suggestion the best. The tab control option was a work-around I was thinking of. Can you elaborate a little on your last suggestion. You state having only one chart and using a button or drop down to change sort order. I'm trying to present a business intelligence perspective (and keep true to the dashboard concept) by displaying multiple graphs with different information on one layout. Am I wrong in thinking this is impossible in filemaker given each layout can have only one sort order.
It's an option that assumes that the only real difference between each chart is the sort order. That may not be the case in your project.
See what happens if you put a single chart object on your layout and use Sort from the records menu to sort your records differently.
Then keep in mind that a number of parts of your chart can be set up as calculations so you can set things up so that some of the labels change the same time that your script changes the sort order. (The script can set global variables to values that are then referenced by those calculations.)
For the time being I implemented your first suggestion. its not ideal because its not dashboard (ish) but its the best i can do for now. For those who struggle with this approach, here is the script I came up with that seems to work: