Does the act of disposing of a portion of the fasting expiation (fidya) money, which was designated for the questioner's family, invalidate this expiation? And do any consequences or expiations result from that?

You are only required to pay the money to those to whom it was sent. If your family is poor, that expiation (fidyah (definition)) is sufficient, according to those who deem the monetary value acceptable for it. As long as you have repented from transgressing and spending the money in a way other than that for which you were entrusted, then "the one who repents from a sin is like one who has no sin."