First of all, I can only answer for California, but I would tell you that all people in the vehicle must be restrained for safety no matter what state you are traveling. Secondly, a cop writes a ticket and the cop is NOT the final word - the judge is the final word.
Take the cop to trial and fight - you surly can find a traffic ticket specialist in Texas - get the www.nolo.com book on fighting traffic tickets! Go for it!
Texas DPS has been pushing their new "Click it or ticket" campaign on billboards, TV and radio ads all this month since school is officially not in session. Everyone riding in an automobile in the State of Texas must have the safety restraint properly clasped. If the passenger is a child.
§ 545.412. CHILD PASSENGER SAFETY SEAT SYSTEMS;
OFFENSE. (a) A person commits an offense if the person operates a
passenger vehicle, transports a child who is younger than five
years of age and less than 36 inches in height, and does not keep the
child secured during the operation of the vehicle in a child
passenger safety seat system according to the instructions of the
manufacturer of the safety seat system.
(b) An offense under this section is a misdemeanor
punishable by a fine of not less than $100 or more than $200.
(c) It is a defense to prosecution under this section that
the person was operating the vehicle in an emergency or for a law
This is another one of those cases where the details matter. The law requires the child to be properly restrained - the question here becomes what is proper? You need to look at the details of the safety seat, how the safety seat was installed, and whether or not the child was properly secured within the safety seat. It sounds like you have decent facts for fighting this one...However, the 16 year old in the back seat could be a problem. Again, something that can be fact specific.