second: だいに（の） (not にだい（の）)
to want to speak: はなしたい (not はなしできたい)
はなしたい can't convey the nuance of "to have always wanted". Also, だいにげんご is not so commonly used in daily conversation. It's more likely an academic term. I would say さらに、いつも母国語以外の言葉を話したいと思っています。（さらに、いつもぼこくごいがいのことばをはなしたいとおもっています。）.
Does
ぼこくごいがいのことば
mean Home tongue?
the last part
はな ｵたいとおもっていま
Totally lost me I see (はな ｵたい hana o tai ----want to speak と to---with おもっています omotte----- to think consider?)
母国語 (ぼこくご) is "native or mother language".
以外 (いがい) is a suffix that means "other than" or "except".
So 母国語以外の言葉 (ぼこくごいがいのことば) is "a second language".
The ｵ there is supposed to be し. The forum sometimes displays characters incorrectly. Therefore, it's hanashitai, "want to speak".
The と is the quotation particle that connects a clause to the verb 思う (おもう).
In this instance 思っています implies that you've been wanting to learn for some amount of time and that it isn't something you just decided now (which would be just 思います [unless I just got those backwards]). It also softens the statement, which you'll often run across in statements about one's self.