I am going to play a life domain cleric paladin multiclass with high charisma. Since life domain cleric already has healing word as a prepared spell, can I cast it with my charisma or do I need to prepare healing word again with paladin to cast it with charisma?
You cast healing word with Wisdom as the spell casting ability
A spell prepared by a particular class is only cast with the casting modifier of that class. Since the healing word spell is prepared as part of the cleric class then you must use your wisdom modifier to cast it.
Each spell you know and prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell. Similarly, a spellcasting focus, such as a holy symbol, can be used only for the spells from the class associated with that focus.
You can't prepare healing word as a paladin. It isn't on their spell list. You must prepare it as a cleric, and cast it using Wisdom.