Rsnapshot filepermission problem with network hdd over raspberry pi

After trying to solve this for days, I want to ask for help here:

I want to make backups with rsnapshot, which usually runs on a server and manages local backups. In my case, I want to run rsnapshot on my computer and let rsnapshot manage my backups on an externel harddrive. This externel harddrive is connected to my raspberry pi and mounted to my computer with following command:

sudo sshfs -o default_permissions,allow_other,idmap=user,IdentityFile=/home/user/.ssh/id_rsa pi@192.168.0.1:/mnt/externelHdd /mnt/backupHdd

Here, /mnt/backupHdd is the local root for rsnapshots backup directory.

Additionally, I want to connect the external harddrive directly to my computer for bigger backup jobs. For this purpose I wrote a script, which mounts the external harddrive either locally or over network with upper command. Afterwards, it starts the rsnapshot job with sudo rsnapshot daily. When the harddrive is connected locally, everthing works fine. When it's connected over sshfs, I get permission denied errors.

Rsnapshot apperently is not allowed to manage files per sshfs, when the files/directories were created with physical connection (different users: local and rasppi). I tried to solve this with the option allow_other and idmap=user but I think there is more to do. So Im asking you guys: How can I give permissions to rsnapshot?

Thanks for any help!

edit:

I get the following error:

/bin/cp: cannot create directory '/mnt/backupHdd/daily.1': Permission denied
----------------------------------------------------------------------------
rsnapshot encountered an error! The program was invoked with these options:
/usr/bin/rsnapshot daily 
----------------------------------------------------------------------------
ERROR: /bin/cp -al /mnt/backupHdd/daily.0 /mnt/backupHdd/daily.1 failed (result 256, exit status 1).
ERROR: Error! cp_al("/mnt/backupHdd/daily.0/", "/mnt/backupHdd/daily.1/")

daily.0 was created when the hdd was connected to my local computer. daily.1 should be created with my hdd mounted over sshfs.