Am I sinful if I give an incomplete statement about the value of money someone swore me by Allah about, in order to preserve family ties, and I did not utter any oath with my tongue?

The basic ruling regarding lying is that it is forbidden, and it is a sign of a hypocrite. However, if there is an overriding legitimate interest or an unavoidable necessity that calls for it, then it is permissible to use ta'ridh (ambiguity/equivocation). Ta'ridh is disliked (makruh (definition)) but not forbidden if there is no interest or necessity that calls for it. It is permissible to swear an oath on ta'ridh if the one asking for the oath has no right to ask the question, in which case the intention of the one swearing the oath is what counts.