And while we are (not really) on the subject of teatree, I'm just going to cut and paste from Wiki on the matter. Everything here is referenced and you can get to the references by following the link to the article. These are all, from what I can see, peer reviewed articles, as opposed to, say, someone's Phd thesis.
"A 2012 review of head lice treatment recommended against the use of tea tree oil on children because it could cause skin irritation or allergic reactions, because of contraindications, and because of a lack of knowledge about the oil's safety and effectiveness.[13]"
"Topical application of TTO can cause adverse reactions at high concentration. Adverse effects including skin irritation, allergic contact dermatitis, systemic contact dermatitis, linear immunoglobulin A disease, erythema multiforme like reactions, and systemic hypersensitivity reactions.[8][14] The National Pediculosis Association in the United States states pure tea tree oil is contraindicated for use by pregnant women and children.[13][15]
Tea tree oil is toxic when swallowed.[14] According to the American Cancer Society ingesting tea tree oil has been reported to cause drowsiness, confusion, hallucinations, coma, unsteadiness, weakness, vomiting, diarrhea, stomach upset, blood cell abnormalities, and severe rashes. It should be kept away from pets and children.[3] Tea tree oil should not be used in or around the mouth.[4] There is at least one case of poisoning reported in medical literature.[16]
Exposure of tea tree oil to air and light results in oxidation of some of its components. Oxidized tea tree oil should not be used.[17] Some people experience allergic contact dermatitis as a reaction to dermal contact with tea tree oil. Allergic reactions may be due to the various oxidation products that are formed by exposure of the oil to light and/or air.[14][18]
In vitro testing of tea tree oil shows that it contains chemicals which are weakly estrogenic causing particular concern for use with children. However in tests, the chemicals which show this effect failed to show absorption into the skin, and evidence of a hormonal effect is therefore considered implausible by an EU scientific committee.[1]
In dogs and cats, death[19][20] or transient signs of toxicity (lasting 2 to 3 days), such as depression, weakness, incoordination and muscle tremors, have been reported after external application at high doses.[21] In rats the LD50 is 1.9-2.4 ml/kg.[22]
Undiluted tea tree oil can cause some hearing loss when used in the ears of non-human animals; however, a 2% concentration has not been shown to have any lasting effect. It is not known whether the same is true for humans.[23]"
Wiki on tea tree
Substitute the word "tea tree" for "terpinen-4-ol" and see how much you want to be wafting it around near your child's mouth. Oh and incidentally, terpinen-4-ol /teatree, from what I can work out quickly, seems to be pretty volatile, meaning it floats around easily. So while applying it locally and topically in 2% solutions is probably fine, at least for adults, I would not personally be spraying it near my kid's head.