Since both are Catholics, your cousin and her fiancé are bound by Church law to marry in the Church. The Code of Canon Law establishes the form of the celebration of marriage which generally "must be observed if at least one of the parties contracting marriage was baptized in the Catholic Church or received into it and has not defected from it by a formal act" (CIC 1117). Marrying in an "independent catholic church" will not satisfy this obligation and the resulting "marriage" will be invalid.
Although they will not incur excommunication for this, a conjugal relationship outside a valid marriage is grave matter and they should not receive the Eucharist until the matter is rectified and they have been to confession. You would do well to express your concerns and strongly encourage them to marry validly in the Church.