Except for the front passenger seat, sometimes seat belts are not available in taxis in Thailand, or they are difficult to operate. If you get into a taxi and cannot find the rear seat belt, as the driver to lift of the rear seat, it's often just underneath the cushion.
There is no legal requirement to use car seats for infants and small children and many people do not even seat belt their kids in Thailand. Accidents still happen and are the cause of too many child fatalities every year. Just because you're on vacation, car seat safety doesn't need to.
If you are traveling with small children, the best option is to rent a car yourself and bring your own car seat. You can buy car seats at some department stores but they are often very expensive compared to what you would spend back at home. If you need to use a taxi while you're traveling, ask your hotel to call ahead and arrange a taxi with seat belts. They do exist, it's just hit or miss as to whether you'll get one if you flag a taxi off the street.