Sandy,
I have not looked at John's link yet, but your daughter is correct in the fact that it can be flown at the same height as the US Flag. But so can all state flags flown on a separate pole. On the same pole the US Flag is on top. I believe that the "codification," for the US Flag states that when multiple flags are flown, The US Flag will be in the Center. Example: US Flag, Texas Flag, POW/MIA Flag all on different ples. The US Flag will be flown in the Center, Texas on the right of the US Flag, and the POW/MIA flag on the left. (This is the US FLAG's own left and right so the perspective is reversed if you are looking at it. Another Example is if your are flying the US Flag on an automobile and another flag. As you sit in the Auto, the US Flag will be on the right. As you look at the Auto from the front, outside, the US Flag will be on the Left. Lot's of motorcyclists get this one wrong.
Now I'll go look at John's link.
From the Texas Flag Code:
Texas State Flag
§ 3100.055. DISPLAY ON FLAGPOLE OR FLAGSTAFF WITH FLAG
OF UNITED STATES. (a) If it is necessary for the state flag and
the flag of the United States to be displayed on the same flagpole
or flagstaff, the United States flag should be above the state flag.
(b) If the state flag and the flag of the United States are
displayed on flagpoles or flagstaffs at the same location:
(1) the flags should be displayed on flagpoles or
flagstaffs of the same height;
(2) the flags should be of approximately equal size;
(3) the flag of the United States should be, from the
perspective of an observer, to the left of the state flag;
(4) the flag of the United States should be hoisted
before the state flag is hoisted; and
(5) the state flag should be lowered before the flag of
the United States is lowered.
Added by Acts 2001, 77th Leg., ch. 1420, § 7.001, eff. Sept. 1,
2001.
Edited: Here is the Government Printing Office
Documentation (A Government site)