It would cost you £31.25 to obtain the following:
- Eastleigh to Hove Off-Peak Return via Barnham for £29.50, available from any ticket retailer
- A change of route excess to the Clapham Junction Not London route on the outward portion of the ticket for £1.75 to the Super Off-Peak Return ticket, available from any ticket office or from the onboard guard (there is no penalty for buying this excess onboard)
You would need to travel on a train that arrives in London Waterloo after 14:00 - the 12:47 from Eastleigh towards Waterloo changing at Woking for the 13:46 towards Waterloo which calls at Clapham Junction would be the first itinerary that would get you to Clapham Junction.
You can break your journey at Clapham Junction - just keep in mind your ticket isn’t valid to travel to or via London Waterloo/Victoria, so you’ll have to change if your train doesn’t stop at Clapham (such as above).
In the evening, hop on a train towards Worthing (whether that’s the direct to Littlehampton via Hove or changing at Brighton) from Clapham Junction. Keep in mind the evening restriction here - you can’t use any trains departing Clapham Junction between 16:00 and 19:09 or Victoria between 16:00 and 19:00.
You’ll switch to the return portion of your ticket when your train calls at Hove and break your return journey at Worthing - simply continue it on Saturday (no time restriction as it’s the weekend) travelling back following the via Barnham route restriction along the coast to Eastleigh.