Looking around briefly on the web it looks like your remote app is using Simple MAPI to seend emails through outlook. This functionality has been deprecated, ie no longer supported, and from your issue, looks liken the R2 upgrade breaks it, thus your error. New apps should use Extended MAPI, note i'm just spitting back what i've read, not a developer who would directly deal with this.
Couple options i would see at this point.
1) i found a hotfix available that may help your issues
http://support.microsoft.com/kb/980681This hotfix is for an issue with Mail merge in Word, but apperently mail merge in word has the same issues with Simple MAPI your having, and as one of the files included is a new mapi32.dll I think that couldd fix all apps that have this issue not just word.
2) check with the compny supporting your remote app, to see if they have a patch or new version of their software which is supported on server2008 R2
3) which i know this isn't fun, but rollback to server 2008 standard, which means a reinstall of everything.