Maybe I'm missing something, but isn't the root folder of www.thisismysite.com and thisismysite.com the same folder, and also the same folder as that for mysite.com? It appears this is a single site with Aliases, not 3 separate sites.
If so, I would expect
Redirect 301 /resource1 http://www.mysite.com/resource1
in the shared directory to cause an error as it will never resolve.
Assuming they all do share a common directory, I might use something like this:
RewriteCond %{HTTP_HOST} ^thisismysite\.com$ [NC]
RewriteRule ^resource1$ http://www.mysite.com/resource1 [R=301,L]
RewriteCond %{HTTP_HOST} ^www\.thisismysite\.com$ [NC]
RewriteRule ^resource1$ http://www.mysite.com/resource1 [R=301,L]
Please let me know if this is wrong!
-BSIS