How do you say someone wants to do something?
How would I say "My mother wants to clean her room."?

I wrote out this, but it seems more like "I want my mother to clean the room"

제 엄마는 방을 청소하고 싶어요.

Is it just a matter of topic and subject marking particles, or am I really missing something here?

Question

How do you say someone wants to do something?
How would I say "My mother wants to clean her room."?

I wrote out this, but it seems more like "I want my mother to clean the room"

제 엄마는 방을 청소하고 싶어요.

Is it just a matter of topic and subject marking particles, or am I really missing something here?

Answer

"My mother wants to clean her room."
-> 엄마가 방을 청소하고 싶어한다.
-> 엄마는 방을 청소하고 싶어한다.

"I want my mother to clean the room"
-> (나는) 엄마가 방을 청소하기를 바란다.
-> (나는) 엄마가 방을 청소했으면 좋겠다.

Answer

"My mother wants to clean her room."
저희 엄마는 엄마의 방을 청소하고 싶어하세요.
* "저희" is more natural than "제"

"I want my mother to clean the room"
엄마가 그 방을 청소해주셨으면 좋겠어요.
* It would be better to use a respectful form.

Answer

Hi! I asked a different forum. I'm not 100% sure about this, but someone said this may be how you say it. 제 엄마는 엄마의 방을 청소하고 싶어요.

Answer

I'm a total beginner, but maybe just take out 제.  
I think there might be a particle to put on 어마 to designate it is her room instead of 제.  
I am looking forward to the answers posted!