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From my research and testing, the behavior that you are experiencing of only being able to grab a sliver of the pie and not move the entire mark is expected. The ability to move an entire mark within a chart is not available in Tableau Desktop but feel free to vote up the idea here: https://community.tableau.com/ideas/4268
I know spatial files can be tricky to work with but typically the reason for the marks to display in odd places is according to the data they represent. The mark (in this case the pie chart) will remain in the same spot unless we change the data.
With that said, you do have some options for what you could do to workaround this:
1. We could create separate sheets for each pie chart and then overlay the pie chart sheets on the map sheet in a dashboard view. This would allow for free movement of the pie charts (using floating objects Size and Lay Out Your Dashboard ) but as you'll notice, the background of the Pie Chart worksheets in not transparent so this might not be the best option (https://community.tableau.com/ideas/6109 )
2. We could also try increasing/decreasing the size of the pie chart to see if this allows for better placement Size Properties
3. Lastly, we can do some testing to modify the data to see if making any modifications to the spatial file allows for the desired placement on the map view
Hopefully this is helpful. Let me know if you have any questions at all!