"She has little children."
Translation:У неё маленькие дети.
not native, but after wrangling with this issue for a while, here's what I've come to understand: the есть is used exclusively when establishing the existence as opposed to non-existence of a possession. So "у меня есть брат" responds implicitly to the question of whether I have a brother or not. "У меня умный брат" (no есть) is something in between "my brother is intelligent" and "I have an intelligent brother." It's not the existence of a brother that was in question, but rather a presumed brother's qualities. I asked about that example somewhere else, and "У меня есть умный брат" is apparently grammatical, but maybe sounds a little odd: something like "I have a brother and also he's intelligent."
So here, есть is decidedly not necessary, since what the sentence is communicating is that "her" children are young, not that she is not childless. A few people here are suggesting that есть should be accepted, and I'm not totally sure about that. But if it should be, I think the connotation would be that we knew nothing about the family status of the antecedent of неё before hearing/reading the sentence.
Hope this helps.
A native speaker here; you are absolutely correct.
"У неё есть маленькие дети" is more like "She has children that are small"; it does not simply describe her children. In fact you can say that if both parties are already aware of her grown-up child/children. In English you you would say "She also has small children" whereas in Russian the use of есть would make it clear in this context.
The same is true of your example, "У меня есть умный брат" - a possible context for this would be if you had already met my not-so-clever brother and I decided to clarify that there are other kinds in my family.
Date20200305 Let's say I have $2000 to my name. If I say I have $2000, you probably don't assume I have it in my pocket, but I do "have" it or own it. It's my understanding that Russian disambiguates this distinction by including есть or not. If you said she had small children, we assume she has small children under her care (excluding есть), not that she has them at this moment in the trunk of her car. Or, when I say I have a girlfriend, you wouldn't assume I have someone else's girlfriend in my basement.
Including есть changes the meaning.