How to backup via dropbox and save 1:1 previews in a seperate directory

What you call '1:1 previews' are not just 1:1 previews but all standard previews. They are what Lightroom uses to show you images in the grid, in loupe view, etcetera. The best way to sync a catalog between two computers is to sync these previews as well, because otherwise Lightroom will need to rebuild them (or at least the ones that changed) each time you switched and that will slow you down. A Dropbox Pro account with 1 TB space is not that expensive. Don't worry about the sync time. Your previews.lrdata is not a massive 300 GB file that needs to be synced in full each time. It's a folder (on Windows) or a 'package' (on Macintosh). A package is a folder disguised as a file. Because it's a folder, only those previews that have changed or are new will sync.

If you don't mind that rebuilding and really don't want to sync the previews, then you could do the following. Place the Lightroom catalog folder in Dropbox. Then use 'Selective Sync' in Dropbox to exclude the standard previews. Dropbox will probably delete those previews when you turn on selective sync, but if you start Lightroom it will rebuild them and then Dropbox should leave them alone. Do this on both machines.