You need to contact an attorney in the jurisdiction where you were given the reckless driving ticket. Ask if that attorney can get your appearance waived, negotiate a plea agreement, and allow you to mail in the required fine/court costs from wherever you are in Texas. Your wife cannot go to court for you. But, if the court will allow it, an attorney may usually make the appearance on your behalf.
You should re-post this question in the state you received the "citation". You may want to seek an attorney there from Avvo.
In Texas, there is a potential for 30 days in jail for reckless driving, so it's not typically considered simply a "citation". Citation is a word which makes me think of a "fine only" sentence range, such as Class C misdemeanors in Texas.
Your court may have more formal procedures in place because your charge may carry the possibility of jail time. Usually, "fine only" cases may be handled without the defendant being physically present.
It simply makes sense to consult with an attorney. You may wind up saving more on travel expenses.
Like my fellow lawyer said, your wife cannot represent you in court. This case is considered the government against you.