First of all, '싶어 하다 or 싶다' modifies 열망 in both sentences. It's not '~어 하다' in indirect speech. Then, you would understand easier the following explanations. '싶어 하다' has a kind of progressive meaning in the first sentence. But, I don't recommend to use '싶어 하다' in this case. (I've been working as an English-Korean translator for years.) We don't say "I am wanting to~" in English. It's exactly the same. In well-written Korean essays, '고국을 보고 싶은 그의 열망은 더욱 더 간절했습니다(간절해졌습니다).' sounds better. However, you should say "그는 고국을 보고 싶어 한다." because it is referring to the third person. You say something on behalf of someone else('그') in this sentence, so it's indirect speech. Maybe you would ask why '~어 하다' in the first sentence is not indirect speech. That's because we don't say something on behalf of 열망. Now, does everything make sense? :-)