"I can't stand their dog."

Translation: Jejich psa nesnáším.

[Kais964773]

Nešlo by : "Nemohu vystát jejich psa." ?

[VladaFu]

šlo, přidám

[MiltonIsCzech]

Jejich psa nesnáším - i can't stand their dog
Nesnáším svého psa - i can't stand my dog
Nesnášejí svého psa - they can't stand their dog? (rather than nesnášejí jejich psa)?
So if it's ME talking about THEIRS we say jejich, but if it's THEM talking about THEIRS we use svůj (or the appropriate form, svého in the case of psa).
Is that correct?

[VladaFu]

Yes, that is correct, svůj and the forms of thereof always relate to the subject of the sentence.