I wanted to chat my friend with "Let's chat together when (after) you are home!". First, I wrote this sentence : "你回家后咱们一起聊聊吧～" // But then when I tried to check my sentence with translation tools (Google Translate and Naver), they added "再" after "后" and thus changing my sentence into this : "你回家后(再)咱们一起聊聊吧～" // Okay, I don't know whether my own sentence is correct or not but... Is what the translation tools said is correct? Should I add 再? And if I should, what does 再 indicate here?
再 means "again" or "continue to". 回家后咱们再一起聊聊吧 means "Let's chat again when you are home". You two may continue what you have discussed or talk about other topics.
Your sentence "你回家后咱们一起聊聊吧" denotes the same meaning as your English sentence "Let's chat together when (after) you are home!".
To me, there are 2 meanings.
1. After you go to home, we continue this conversation. 2. After you go to home, we do more conversation.