For protecting the leather saddles from rains, both Brooks and Berthoud sell covers for their own saddles:
Brooks, and Berthouds
1 (the older version? But it's definitely cheaper),
2 (the newer version?). When not in use, you can fold them and stash them in your saddle bag. Brook's is big enough to cover a Berthouds, but the reverse is not true. The newer Berthould cover is more form fitting.
Although I have no experience in your use case, I would put a rubber band or bungee cord to tighten the cover over the saddle when transporting the bike on a car. But better yet, put your bike in your car to get the best protection. That usually require the backseats to be folded down, even on a big SUV. Or the wheels need to come off.