My problem is, how can I make rsync to switch to another harddrive automatically if space on the first one is full? Is there a simple way? Or even a way without using rsync?
I don't think what you propose is achievable (with just rsync) and/or sensible. Rsync synchronises objects in two locations. You should probably think about solving this on a lower level.
First of all, if this is how you back up your data, by splitting it randomly between two disks, you effectively double the chances of your backup becoming incomplete if one of the devices fail.
If you really don't care about that (depending on the data importance it might be a pretty bad idea), you could:
in short (I named the Volume Group 'vg10' and the Logical Volume within it 'backup'):
Keep in mind that you'll need both disks connected to be able to mount /mnt/backup and that this doesn't give you ANY redundancy.
I don't know your scenario but I'd go with at least a RAID1 setup for my backup.