temporarily seal leaky pipe under sink?
Nice Pics.  For a good temp fix on this drain line, I'd recommend "Seals All". This avail at any hardware store.  As far as a permanent fix, you may not have to deal with the copper, but you will have to cut the PVC in an area where you can fit a coupling and replace the parts to the copper.  Thread on  the new adapter to the copper and use a PVC coupling to reconnect to the rest of the drain.  This will mean some cutting, primer and PVC cement.