How to use particles in ~고 싶다?
고기를 먹고 싶어. = I want to eat meat.
가족을 보고 싶어. = I want to see (my) family.
한국어를 배우고 싶어. = I want to learn Korean.

I learn ~고 싶다 sometime ago. And I always use 을/를 like the examples above.
But I found that 가/이 is also used too.
엄마가 보고 싶어. = I miss (my) mom.
Why? Shouldn't it be "엄마를 보고 싶어"?
Isn't the meaning become "My mom (is the one who) miss/want to see (something/someone)?

Also how if I say, "내가 엄마를 보고 싶어."?
Is it mean "I'm [not you, not my father, who] miss [my] mom."?

Question

How to use particles in ~고 싶다?
고기를 먹고 싶어. = I want to eat meat.
가족을 보고 싶어. = I want to see (my) family.
한국어를 배우고 싶어. = I want to learn Korean.

I learn ~고 싶다 sometime ago. And I always use 을/를 like the examples above.
But I found that 가/이 is also used too.
엄마가 보고 싶어. = I miss (my) mom.
Why? Shouldn't it be "엄마를 보고 싶어"? 
Isn't the meaning become "My mom (is the one who) miss/want to see (something/someone)?

Also how if I say, "내가 엄마를 보고 싶어."? 
Is it mean "I'm [not you, not my father, who] miss [my] mom."?

Answer

In this case, 이/가 is different from the one which makes a noun a subject like 내가.
It is used to emphasize the object with the expression -고 싶다. 
So in 엄마가 보고 싶다, 엄마를 is the basic form and you want to emphasize 엄마를, it becomes 엄마가.
고기가 먹고 싶다. 가족이 보고 싶다. 영화가 보고 싶다. They are all okay. I think it goes well with 먹고 싶다 and 보고 싶다. 한국어가 배우고 싶다 is not wrong but doesnt sound natural.

Answer

I agree with Sleepyhead. It just doesn't sound natural. You can say it, too.

Answers · 2

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