There are 4 cases of 다니 in your question. 1. 다니 in 네가 하고 싶은 말이 그게 다니? 다니 is composed of 다+이(다)+니. 다 means "all" 이다 means "to be" 니 is an ending particle for question. 2. ~다니 in 왔다니 기뻐요 다니 is a short form for 다고 하니까 "A다니 B" Means "(because) I heard A (so) i feel or think B" A = quotation that is the reason or basis for b B = speaker's feeling or judgement 3. ~다니 in 그는 언제 떠난다니? 다니 is a short form for 다고 하니 It is used for question of indirect quotation. 4. ~다니 in 여기서 자네를 만나다니. Use if you’re surprised at or can’t believe something you just heard. Used to repeat the relevant info while expressing your surprised feeling at that info. Equivalent to “Really? I can’t believe…”

I can't exactly answer your question because I am curious and unsure myself~ But for your first sentence, the use of 다니 is not what you are asking 네가 하고 싶은 말이 그게 다니? 다 meaning "all" and 니 being used as and sentence ending like you can also say 네가 하고 싶은 말이 다야? so in this sentence the use of 다니 is not the same as the clause ^^ Hope that made something a bit clear~