Actually, it should be "I don't begrudge you your holiday."
To begrudge means to give reluctantly or with envy. In this case, the person speaking doesn't mind the other person taking their holiday; he doesn't have any ill feelings about the person taking his holiday.
Her boss was reluctant to respect the employee. Perhaps he thought less of her because she was female, of because she didn't have a college degree. In any case, he was prepared to dislike her and the job she performed, but because she did it so well, he had to respect her in the end.she won the grudging respect of her boss
Student or Learner