We applied for visa (tourist)extension,and the
reply was to send all necessary documents before September 9, 2003.We sent all the requirements, but no reply yet from the immigration. We really have to see my mother, can we travel to another state during this process? We have state ID'S.

i am sure that everybody are free to travel from state to state within the US.

Keep the notice of receipt for that application as the proved that you apply for extension of time, and also it was said reply before September, so just wait the response before the date given. If you don't receive anything a week before that date, call BCIS or visit BCIS personally for further quieries.

I'm not a lawyer, act accordingly.