I saw two reasons.
In case of Diya, in a typical patriarchy, he is expected to provide and protect her. Her taking up a job where she needs to sacrifice 12 years of her life reflected badly on him as a father.
If it was just worry for her happiness, he would have been more worried about her than her marital status (resultant taunts he got from various people).
But for him the reputation of him as doing his duty as father counts more. I am not blaming him for it. He is bred in that environments. He could not forgive himself for letting that happen.
And in case of Ratan, it was him who was doing mistakes and it easy to forgive others than forgiving yourself.
One more thing I noted it that Ratan is like the son which he never had and that also is a reason his apology is enough for him to melt.