I recommend you to use file synchronizing tools. File system level solution to your problem may not be feasible. Check out unison and conduit. As I understand you already have a copy of files in your primary computer. Here is the work flow that i use:

1. Work and change files on PC_1. After you are done synchronize them to your USB Stick.
2. Connect the USB stick to your PC_2 and synchronize the content to your PC_2.
3. Work and change files on PC_2. After you are done synchronize them to your USB Stick.

Synchronizing will be very fast because only the changed files will be rewritten.

I recommend you to use file synchronizing tools. File system level solution to your problem may not be feasible. Check out unison and conduit. As I understand you already have a copy of files in your primary computer. Here is the work flow that i use:

1. Work and change files on PC_1. After you are done synchronize them to your USB Stick.

2. Connect the USB stick to your PC_2 and synchronize the content to your PC_2.

3. Work and change files on PC_2. After you are done synchronize them to your USB Stick.

Synchronizing will be very fast because only the changed files will be rewritten. Also you can write mount and unmount triggers that will automatically make the synchronization.

For a file system solution you can look for some FS with Copy On Write attribute, e.g. btrfs. Taking snapshots and syncing them may be faster and more effective. But I couldn't find any implementation yet. Also working on file system level will not ease your way on conflict resolution.