This is an old thread but to reply to the OP--there are some oils that act as um...something that disrupts hormones, and so there can be caution about using them too much with kids. Also some people have fragrance sensitivity so it's not universal--they could also get overstimulated by strong smells.
There are some oils that have been studied for stress relief--I remember seeing bergamot as one of them, and it did seem to calm people down.
Bergamot is what is in earl grey and it's a citrus.
Anyone into oils should probably try to stick to reputable producers, since they would be easy to counterfeit. They aren't super cheap (some are cheaper than others).
Some oils are caustic and should be used with caution--most people recommend diluting essential oils with some carrier oil if you're going to apply to body.
Oils are used for different things--most can be used for smell, but tea tree is generally used medically as an anti-fungal, anti-bacterial thing, and there are products that use tea tree in fish tanks etc. Neem also...I wouldn't expect to find it in an essential oil section, but it's used as an insecticide.
I think bergamot is a pretty safe oil for relaxation. A lot of people also like to use lavender flower oil (though I think that does have some hormone impact).
Ylang Ylang is a less expensive floral oil that's similar to Jasmine (true jasmine is very expensive, along with true rose).
You can also buy vanilla oil--some of the relaxation is psychological, like vanilla might remind you of something your granny used to cook (I think it tends to remind people of maternal warmth). It's also not super expensive.
Magnesium is good for stress relief if you like to take baths--you could get some epsom salt and then put a few drops of a pure essential oil into the salt and mix it around, and it might disperse well.
Or you can just put it on a pillow or you can put some on your wrist like perfume (though they recommend mixing with a carrier oil like almond oil or even olive oil). There are lots of ways to use it.
