Francisco, your second example is correct. You could also say that she is replacing her old wardrobe FOR a new fitted cupboard. Some more examples: (A) the bumbling English professor is being replaced by a more competent one. (B) The mechanic decided to replace the old, malfunctioning engine with a new, fuel-injected engine. (C) The dog feels as though he has been replaced by the cat. (D) The little girl replaced her tiny tea set for a much larger one.

I would say "replaced with"

You use "by" if the verb is in the passive voice. ("My mother's replaced her old wardrobe by a new fitted cupboard." is incorrect - it actually makes no sense.) You use "with" if the performer of the action is neither of the objects in the replacement. ("My mother's replaced her wardrobe with a new fitted cupboard." makes sense.) You don't use a preposition if the object which takes the new position is also the subject. Some dictionaries will give sample phrases. http://www.thefreedictionary.com/replace