Hello @Matt Fortune
When the user is asked to enter credential to open the remoteapp, what is presented in the logon box?
Not all browsers support Single-Sign-On to a RDSH from Web Access.
This thread might help:
Remote Desktop Services - Users prompted twice when launching remote App
"there is no way to stop the two credential prompts for non-IE browsers. One possibility is to have people save the .rdp file to their desktop and then set it to save the password, although this may not completely eliminate the prompts. Downside is the file would be static and if you ever make changes people would need to re-download a new version and save it to their desktop again. And password changes (if you implement those) would affect the experience too."
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Best Regards
Karlie