Mate it depends on what type of battery it is and how old it is. If it is from Battery World, still in warranty and they have offered to replace it at no cost, why not go with that??
Then you can start afresh with how you maintain the battery.
The fridge is a heavy drain for any type of battery and engine alternator charging is just not going to keep the charge up unless you are motoring all day every day.
I am just spit balling here but say the fridge is efficient and about 60 litre capacity, I think you will need about a 120 amp hour deep cycle battery to run it and a minimum 80 watt solar panel to keep the battery charged.
That battery should be dedicated to the fridge. Then you need another battery for start and house load. If you have all LED lighting a 100 amp hour battery should be ample.
Boat batteries sit idle for long periods and benefit from being charged up with a battery charger as often as possible. It appears you do not park your yacht on a marina often so lugging the battery ashore for charging is necessary. Your battery charger should be a minimum 8 amp unit.
A C-Tek 10 amp charger will cost you $370 if you shop around and get trade price and a 15 amp unit is only a little more. These are "Smart Chargers" which is mostly all you can buy today as opposed to transformer chargers.
Battery World sell an "AusCharge" unit, 1 to 8 to 12 amp charger, one of which I have just bought, that through them carries a 5 year warranty for $219.
The thing to keep in mind with batteries is that no matter which type they are, fully discharging them buggers them big time. My mate who lives aboard quite a lot has Century Marine batteries of which he speaks highly describing then as a cross between a start battery and deep cycle.
Marine electrics is all done with smoke and mirrors.