"Mom has a table at home."
Translation:У мамы дома есть стол.
Ok, so... what's the deal? My answer was "У мамы есть дома стол." There's discussion here about what some word order emphasizes and what is perhaps "awkward". But is it incorrect?
And if the (currently primary) "У мамы дома есть стол" sentence means what I think it does, it's problematic both ways. Indeed, the English doesn't imply "at mom's house", it's "at home". Those are two different things.
If the "at home" is not an essential part of the Russian, then "There's a table at mom's house" would be better. If it is... I don't know. Something awkward like "There's a table at mom's home" or accepting that something gets lost in translation.
У мама(-a+ы) дом(+а) есть стол
У (genetive genetive) есть (nominative)
У мамы дома есть стол.
That would be the locative case, e.g. на столе (on the table). In addition to locative, so far we've learned nominative (dictionary form: стол) and genitive (столы) and without knowing it also a bit of accusative (for most masculine and neuter nouns the same as nominative). The construction here requires a nominative стол.