I was able to solve the problem by using the getTimestamp.bat from dbenham: http://www.dostips.com/forum/viewtopic.php?f=3&t=4847&p=27422#p27422
This is the only working batch file I could find that is able to calculate the date of yesterday (potentially any day for that matter).
It is probably the only working one, because all others (and also all of the ones linked in the regarding StackOverflow threads) don't take locale settings into account, so they didn't even start for me.
call getTimeStamp -od -1 -f {dd}.{mm}.{yyyy} -r dt
rem Copy file including timestamp
xcopy "\\unc\folder\fileToBackup.accdb" "\\unc\folder\backupedFile_%date%_%TIMESTAMP%.accdb*" /Y
rem Delete yesterdays file
del "\\unc\folder\backupedFile_%dt%_%TIMESTAMP%.accdb*"