“甘い” is a little different in Japanese and in English, I think.
What I thought was “he is indulgent to his daughter” would be really a good word I think.
And then there is another one you wrote was “he is too tender to his daughter”, but “tender” is a really soft image.
I thought maybe this will not be so good.
And you also said “too kind”, but you never be kind to your daughter, or you would be kind to other people, who are not in your family.
So I think “kind” would not be a good one either.
And “generous”, OK, “generous” might be not so bad.
Maybe you can be generous to your daughter.
But I don’t think I would be generous to my father too, or to my mother.
I guess they are not wrong, but if it is your daughter, I wouldn't use these words.
I will use “indulgent”.
There is another one you wrote, “he accepts anything his daughter wants”.
I thought “he listens to his daughter’s demands too much” is probably an “甘い” father.
And you said, “I think he needs more discipline for her”.
So I said, “I think he needs to discipline her more”, like “しつけする” her more.
That was a good one too.
And the first time when I saw “甘い”, was like “甘やかす” was my first image of “甘やかす”.
So “甘やかす” would be not so bad in Japanese.
“He would 甘やかす his daughter or son”, which means maybe whatever they want, maybe the father would buy anything that they want.
But in English, you can say “he spoils his daughter”, but “spoil” would be a really harsh meaning.
And it would be like, if you really spoil the child, that child would be a very bad girl or a very bad boy, maybe might be stealing something from someone.
So “spoil” is maybe too much. No, that’s too much.
“甘やかす” is probably a little more tender maybe, a softer image.
So I thought. But if the child becomes really bad, you can say “spoil” too.
“He spoils his daughter. That’s why she was arrested. That’s why she is in the jail now”, like that.
So “spoil” would be too strong, I would say.
indulgent 【形容詞】 〔…に〕甘くて
discipline 【名詞】 しつけ
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