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「お礼に一杯おごろう。実は今日、給料が入ったんだ」
「そうですね、嬉しいお誘いなのですが……」
「……娘が心配しちゃいますので」
Context: The above two characters have been out for a while and the guy offers to treat her with his pay. She declines because:
1) Her daughter will be worried about her 2) She is worried about her daughter
I believe its 1) as I think 心配なので would have been used for the other meaning but I am unsure.
Yes, 娘が心配する means "(my) daughter is worried (about someone else)," whereas 娘が心配だ means "(I am) worried about (my) daughter". (EDIT: The latter expression using the (na-)adjective is in the same vein as 猫が好きだ and 猫が欲しい)
So 娘が心配しちゃいますので in this dialog means "(If I go home late) My daughter will be worried about me, so... (I can't go with you)."
