Hi Saquita...I've been helping a group of parents with autistic children and they have been using turps to good effect for their kids. The dosage for a 3 y o would be between 1/4 and 1/2 tspn of turpentine taken together with a teaspoon or two of castor oil. This protocol should be used only twice a week.
I've also discovered that using castor oil with turps is a key factor in the protocol. The turps will kill all manner of pathogens and parasites but will not harm the beneficial gut flora. The castor oil is necessary because it helps to spread the turps throughout the whole area of the intestines for a better and more thorough all-round effect.
I think that perhaps your child's gut may be overrun with pathogens and so the turps/castor oil would be a good protocol to follow.
Other protocols that you can also investigate and consider for your child are supplementing Boswellia(Frankincense) and/or undecanoic acid(which is derived from castor oil). Frankincense is called shallaki in Ayurvedic medicine and they use it widely in Ayurveda for gut problems as well as for arthritis.
There was also a mother in the autistic parents group who successfully and completely healed her child back to normal(according to her ATEC scores). One of the child's main anti-parasitic protocols was taking cinnamon, clove, raw garlic and tumeric mixed with ghee or clarifed butter several times a day with food. This protocol kills both parasites and pathogens. The key point in this protocol was that she used ghee -- a saturated oil -- as the carrier medium.
Many people miss the importance of taking nutrients in the best way possible by using the correct carrier medium. Notably she took all those herbal ingredients mixed with ghee because all the active ingredients within the herbs/nutrients themselves were probably oil soluble and not so soluble in water. That's why she was so successful with this protocol. You could also probably use coconut oil as a carrier substitute for the ghee. Virgin coconut oil also kills a wide variety of enveloped pathogens as well.
Also please be aware that if your child has a widespread gut infection and takes the turps/castor oil protocol then she will probably suffer a Herx or die-off reaction with accompanying strange or hyper behaviour. After a widespread pathogen/parasite kill in the gut, with consequent temporary release of further poisons into her gut(from the killed pathogens/parasites), these poisons will be temporarily absorbed into her blood which may perhaps cause some strange or hyper behaviours. This is normal and unavoidable and should abate after a short while after her liver eventually removes these die-off poisons from her blood.