Hi Marcia,
The safety of Guests and Cast Members is the #1 concern at WDW. They do not issue wrist bands. Instead, there is a Cast Member stationed at the entrance to each queue (especially those with height requirements). If they think your daughter's height is close, they will measure her. Depending on the attraction, she will pass a couple of other Cast Members (if not more) along the way. If they think its close, they may indeed remeasure her. If she doesn't meet the requirement according to their measurements, she will not be allowed to board.
In order to avoid heartache or meltdowns, you can see a list of height requirements at all of the parks by visiting the Traveling with Little Ones section on the WDW website by clicking
here. On the right side of that page, you will see a PDF file containing a complete list of height requirements.
Also keep in mind that just because there isn't a height requirement on an attraction doesn't mean its suitable for everyone. Haunted Mansion is very dark and may frighten some children. You know your daughter better than anyone. If you have any questions about any particular rides, let me know - I'm honored to assist you!
Wishing you many magical memories :-) Allison