"I show the children the small spiders."
Translation:Eu le arăt copiilor păianjenii cei mici.
It's not compulsory here, but the sentence sounds slightly more formal without it. You are generally better off using "le" than omitting it.
Because that would be indefinite: "I show the children small spiders." "Păianjenii cei mici" is more like "the spiders that are small."
So, you make sure you show the children the small spiders and not the big spiders because you don't want to frighten them.