How should I rebase a clothesline post on sloped property?
You said that one end is attached to the house, and the other end is attached to a post which is attached to a vehicle shed.

Is there any reason why you need a post on the vehicle shed end?  Could you attach the line directly to the shed (e.g. with an eye-bolt)?  That would seem like the simplest solution.

ETA:  Given the slope of the land, maybe a metal post attached to the side of the shed would be a good option?  Something similar to what you might use for a lamp post?