I think you need to get real medical help, to determine if she's "holding it in", or if she has a physiological problem with bowel movements.
If it can be determined that she is purposely withholding, then you probably need to get psychological counseling. But honestly, it's usually a physical problem.
Rockrose is correct. She is holding it in because she is constipated and it really hurts her to go and she wants to avoid the pain.
This is a link to an article that pretty well covers all the bases.
http://www.practicalgastro.com/pdf/November02/LoeningBauckeArticle.pdf
Is your child potty trained? I had a problem with my son and constipation also. He was on miralax for probably a year, once he got over being scared of the toilet he hasn't had any constipation issues!