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How to explain the difference to someone who's not a native Russian speaker? Example:

  • Ты любишь свою маму?
  • Ты любишь твою маму?

The second example sounds a bit wrong.

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Свой is used as a possessive pronoun for the agent (not necessarily subject) in the sentence.

  • Я люблю свою маму
  • Солдату приказали принести свою винтовку (солдат is not a subject but still the agent for принести. There is no agent for приказали, so своя unequivocally refers to солдат)

If there is more than one agent in the sentence, it can be somewhat confusing what does свой refer to, though usually the last mentioned agent is assumed.

  • Папа попросил принести свой чемодан (папа is only the agent in the sentence, so it's dad's suitcase)
  • Папа попросил маму принести свой чемодан (папа and мама are both agents to different verbs, so the sentence can be parsed both ways, but most people would assume it's mom's suitcase)

If you are using a non-reflexive possessive pronoun, it should either refer to a third party (он любит его маму "he loves his (someone else's) mom") or resolve the ambiguity introduced by multiple agents (папа попросил маму принести её чемодан). Otherwise it would sound a bit wrong indeed, as you have correctly noted.

3

That is easy.We use свой(свою) with all personal pronouns.Here mom is a close relation of the person ( here the subject ).

Я люблю свою маму. (I love my mum) Ты любишь свою маму?(Do you love your mom? )Мы любим своих мам.(we love our moms)

That is the case when in English the subject corresponds to the possessive adjective. We don't say ты --твою. When it doesn't, we use possessive adjectives according to the meaning. Mom is not a relative of the person (the subject ).The agent is not necessarily a subject in the sentence.

Я видел твою маму вчера. Она видела мою маму.

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