You're making things more complicating. The acyl chloride reacts through the claisen condensation with the acid, since it has the alpha carbonyl alkyl group, this can be deprotonated with a base and serve as the nucleophile. Be sure to remember that this acyl chloride is the reagent that is not listed in your original problem but suffices for the requirement of a two carbon compound. Be sure to draw it out correctly.
The acyl chloride with the ester does not react through a claisen condensation, it is not technically called the claisen condensation although it has similar mechanisms. The difference is in the elimination aspect, the chloride is eliminated after the deprotonated alkly group attacks the carbonyl carbon of the acyl chloride, subsequent rearrangement eliminates the chlorine. You should know that this is a addition elimination reaction of carbonyl compounds. Review transacylations in your organic chemistry book.
Hope this helps.