How can I fix this battery problem without spending a lot of money on this car.

Hello! Electrical issues, especially on luxury vehicles, can become complicated. At the least, you'll want to take it to a local certified shop and have a simple charging system diagnosis performed. This would be the first step in discovering if it's just the alternator, or something deeper. Deeper than that would require additional diagnosis, but at least you'd have a better idea of the rabbit hole before going forward. It would still be cheaper than throwing parts at it, though! http://repairpal.com/mercedes-benz-repair-in-port-jefferson-station-new-york-11776