YOU SAID:

my mother said I must be home by noon

INTO JAPANESE

母は私が正午までに家に帰らなければならないと言った

BACK INTO ENGLISH

My mother told me that I had to go home by noon.

INTO JAPANESE

母は私に正午までに家に帰らなければならないと言った。

BACK INTO ENGLISH

My mother told me that I had to go home by noon.