You are correct that vitamins are not regulated like medications are regulated by the FDA. This means that labels and claimed benefits of various vitamin preparations can be misleading or inaccurate. It is best, as a rule of thumb, to stick to major, trusted brands.
At the same time, it is important to realize that most children don't actually need vitamins. In the United States, it is quite rare for children to have vitamin deficiencies, since many foods, such as milk and cereals, are fortified. This even includes toddlers who are very picky with what they choose to eat!
There are a few exceptions to this generalization. Breastfed infants under 1 year of age should be supplemented with vitamin D, as breastmilk does not have much vitamin D. Enfamil Tri-Vi-Sol is one trusted brand, but there are others.
Similarly, some breastfed infants will also need iron supplementation starting around 4 months of age, as breastmilk is also low in iron. You pediatrician
can help you to make this determination at the regularly 4 month check up.
The final exception to 'most children not needing vitamins' is for children who have any sort of chronic medical condition; these children often do need vitamin supplementation, and this is an important issue to discuss with their pediatrician.