Is it permissible to give my relatives who are affected by the aggression in Gaza a portion of the cash designated for those affected there, given the difficulty of finding the most severely affected in these circumstances?

The most needy and deserving recipients of charitable donations must be sought out. Acting upon the dominant assumption is sufficient. It is obligatory to observe any conditions stipulated by those who donated the funds, if they conditioned their disbursement to the most needy. Otherwise, it is permissible to give them to any needy person, even if they are relatives.