"아이야 먼저 가 (어기야 디여라차 어기야디야) 되찾을꺼야"
=> "아이야 먼저 가 ... 되찾을 거야" (translatable part with standard spelling)
Translating loosely, it's like "Kid, I let you go, ... but I'll get you back".
What's implied is "If you really want to leave me, I'll let you go now. But I'll get you back eventually because I still love you all the same".
The "어기야 디여라차 어기야디야" part is a "work chant" with no apparent meaning.
When people do hard work together, they often chant such lines to get their spirit up and to help synchronize their movement.
Here it might symbolize the pain and sadness going through the speaker's mind.