I don't know about Miyazaki dialect but found on the net that てげよだきい (tege yodakii) means "very much a bother" when one is not willing to do something.
てげ tege means very, really, awfully よだきい is a bother, pain, trouble, etc. that makes people feel reluctant, unwilling, etc.
In standard Japanese it would be すごくめんどう sugoku mendou, or とてもめんど(う)くさい totemo mendokusai.