"Dad has a brother and a sister."
Translation:У папы есть брат и сестра.
Speaking from my humble understanding here. It depends on the message you are trying to convey. If you want to stress the action of 'having sth', then use есть. If not, у + X + Y works just fine.
-У тебя есть сын, да? -Нет, у меня дочь!
In this first example, the person is stressing the fact that they have a daughter, not a son, i.e. they are focusing on WHAT they have and not whether or not they have it.
-У тебя нет дети, да? -Да, у меня есть сыновей!
In the latter, the stress is on the fact that the person does indeed HAVE sons, without focusing too much on details like number or maybe even gender.
As a final hint, remember that есть means something like 'to exist', so the literal meaning of 'у Х есть Y' is 'Y exists by/close to X', that is, 'X has Y'. That should help you understand what part of the message you want to enhance.
From what I understood, to show posession in Russian, you write у SUBJECT есть OBJECT.
"Though Russian does have the verb 'to have' (иметь), it is rarely used. Instead, Russians use the following construction to say "I have X": У меня есть Х. This literally means, 'By me exists X'."
Duolingo forces you to include "есть" in many of these posession sentences. It's technically correct and definitely good habit, but otherwise perfectly acceptable to omit the есть in day to day conversation (EG, "У меня новая машина"). Best not to put the cart before the лошадь, though, and learn the rules before you break them.