@zzz2 , there is no relationship requirement for a gift to be considered a gift -- only (a) the donee has to agree to accept the gift ( inwriting or by action ) and (b) there is no quid-pro-quo i.e. no requirements that will materially benefit the donor.
Yes your mother can indeed give a gift to your wife and the same rules discussed above applies to her also ( reporting, FBAR, FATCA and basis ).
pk
