Wassalaam,
You shouldn't doubt the sincerity of your wife's being a Muslim. She probably doesn't understand this issue very well. Fact is, I didn't understand it either until I learned about the way marriage works in Islam and what is considered adulthood.
The child, boy or girl, in Islam, is considered to have reach puberty based on certain signs, such as pubic hair, a girl's first menstruation, their reaching the age of 15, etc. That is when a child becomes an adult. Thus, a child who reaches the age of 15, or who has obvious signs of reaching puberty (as scholars explain in good detail), then they are considered an adult.
A girl can be married off before they reach puberty, but their marriage is not consummated until they reach adulthood. The age at which a child, let's consider girls specifically, could be from anywhere from the age of 15, to as early as 8 years of age. Taking this lower limit into consideration, Hazrat Bibi Ayesha (ra), was 9 years old, according to many different Ahadith, when she was taken from her house, and brought to the house of the Holy Prophet (saw) to complete the marriage by consummating it. She was seen to have signs of puberty, such as her being somewhat sick, her hair falling out, etc. Many Ahadith say she was breathing heavily, which might have something to do with this. Maybe someone who understand female puberty could better explain this.
Besides this, I have seen arguments where she is considered to have been as old as 12 years of age, based upon what other Ahadith say. I don't know if this is in solar years or lunar years, if lunar, then she could even have been 11.
The point is that young girls, prepubescent, cannot consummate their marriage, but they can be married. When such girls, prepubescent, are married to men, their parents can do this for them without their consent. But when those girls come of age and reach puberty, they have the choice to either accept that marriage or reject it. Thus, Hazrat Bibi Ayesha (ra), according to Islamic law, did have a choice. But we all know how righteous she was at a very early age, and that Allah had created her as a holy and pious woman, the Mother of the Believers. Thus, she definitely agreed to her marriage to the Holy Prophet (saw), and there are so many indications of how much love she had for the Holy Prophet (saw), and how much love he (saw) had for her in return.
The other thing to note, is that early societies had different conceptions about adulthood. Adulthood for Western people is the age of 18 years for people, but this is their own fabrication. The Holy Prophet (saw), the Prophet and Messenger from Allah, had it revealed to him what it means for a human to be an adult. Thus, we take our knowledge of a child's turning into an adult from Allah's Laws, and not the man-made laws about the age of consent and adulthood. A Muslim doesn't rely on man-made laws, but they obey the laws of Allah when man-made laws contradict His Laws. This is because when disbelievers are in rule, and they make a law against the laws of Islam, then we Muslims have full right to disobey that law and not be held accountable for it from Allah. The disbelievers can do whatever they want to us in that case.
Back to the point, adulthood is clearly described by scholars. I am not aware if there are disagreements on this, but check up on the Fatwas or the books on Fiqh which explain adulthood. This is the real issue, but I think from what I have stated, you should be able to explain your wife's misconceptions. If she is a Muslim, and she has full faith in Allah, then she has to accept Allah's Laws about who is and who is not considered an adult. Also, she will have to accept that girls get to choose and consent to a marriage when they become adults.
