Does one say мою in this sentence because if one were to use свою it would connect back to the object его?

Мальчик попросил у меня карандаш, потом я попросил его помыть мою машину.

If this is the case, then would these be translated correctly?

Я попросил её заправить мою кровать.
I asked her to make my bed.

Я попросил её заправить свою кровать.
I asked her to make her (own) bed.

Я попросил её заправить её кровать.
I asked her to make her (someone else's) bed.

Мама попросила меня сделать свои задания.
Mom asked me to do her (mom's) homework.

Мама попросила меня сделать мои задания.
Mom asked me to do my homework.

Мама попросила меня сделать её задания.
Mom asked me to do her (someone else's) homework.

How would you translate these?
Dad asked him to clean up his (the boy's) room.
Dad asked him to clean up his (someone else's) room.
Dad asked him to clean up his (the dad's) room.