yes, you are right. "yong yuan" here is one word, it can't be separated. means "forever". "zai yi qi" is a phrase, means "stay together" .

What language are you learning? Cantonese or Mandarin? Anyway, your sentence is Mandarin for: "I hope we can be together forever."

Could I translate the sentence in this way? "Xi wang wo men yong yuan zai yi gi!" "I hope we will be able to stay always together!"...? I should like to know the rule about that "yuan + zai". Waiting for a kind reply, I send you my best regards. Claudio