You should contact a lawyer who specializes in juvenile and criminal law immediately. The state determines whether to pursue charges and can continue to pursue the case regardless of whether the alleged victims want to press charges. The juvenile system has several options for disposition of the case which can include removal from the home, hence you should contact an attorney as soon as possible.
A dismissal for continuances is only possible when the State takes such continuances and then exceeds the amount of time allotted by the speedy trials statute. Continuances taken by the defense are not counted towards speedy trial calculations. If he has hired an attorney he should discuss his concerns with his attorney.
You should contact an attorney immediately and not post any further information regarding this matter. You may have further exposure for being charged with a misdemeanor or even felony offense. Because of the false name -- your case is not necessarily an "easy" traffic fix anymore.
You misunderstand what the statute of limitations is. It is the time period in which charges must be filed. Upon conviction, your record is permanent and public unless a petition for expungement is granted. A petition for expungment may not be filed until 5 years after post release is completed for a level 4 offense.
You should contact the police department and make a report of the identity theft in both the jurisidiction your husband resides and the texas local department as well. Johnson County KS in particular prosecutes these matters severely. The report of the theft will be encessary to resolve any credit or tax issues caused by the theft, and law enforcement should have victim services that will help direct you.