Four year old girl with dramatic sensitivity on her bottom

My four year old daughter was diagnosed with SPD last year when clothing issues took over our life. Since then we have developed strategies to manage many of the issues, except for her" bottom" , I.e her crotch. She cannot wear underwear at all, of any type. Strangely, she will tolerate swimsuit or leotard while she is engaged in the activity although getting into them is usually difficult. Seems like very light contact is the problem and along those lines she rubs the front of her bottom frequently and vigorously. She just recently explained that rubbing "stops the tickling feeling". She was adamant that it was not itchy but tickly. We have of course confirmed with pediatrician visits that there is no purely physical reason for this, i.e. infection etc. All seems to fit into desensitization mechanism.

But, rubbing her bottom is socially unacceptable in public and to this degree. We have discussed that she can do this only in front of mom or dad and that if others are present, she must go to a different room. Some days this can take a very large amount of time and really strains our relationship and my patience despite thee fact that I know that this is a "real" sensation. I have learned so much about SPD recently, but can find nothing about this specific tactile issue. Additionally, she is so clearly miserable some days with this sensation that I want to cry and want to do anything to help her manage it better. Are there any suggestions?