She's in Kindergarten.
So, during the school week, while she is in school 5-days a week...is she also going to the bathroom at school all the time frequently and washing her hands, THAT much, at school?
While in school, the kids don't go to the bathroom that frequently as it seems she has to, nor do they wash their hands all that frequently. Yes, they can go to the bathroom at school, when they have to and the Teacher typically lets them. And then sure, a kid will wash their hands etc. And they go pee also before lunch and wash their hands before lunch.
So at school.... is this also a problem?? And if so, has the Teacher told you... that your daughter goes pee too often and always has to wash her hands that frequently?
Also, in schools, they don't have hand sanitizer in the bathrooms. They have soap to wash hands. So while your daughter is in school, is she using her own hand sanitizer? Or washing her hands in the school bathroom, using the soap that the school uses in the soap dispenser on the wall?
At least in my kids school, they do not put hand sanitizer in the student bathrooms. It has soap, in it.
2) Then the other issue is: her skin seems sensitive and when using hand sanitizer it is too harsh for her skin. Hand sanitizer has alcohol in it and fragrance. It dries out the skin. So don't use hand sanitizer for her, and get the type that does not contain, alcohol or fragrance etc.
3) And the other "problem" is: she gets pee on her underwear when she goes to the bathroom. Well, this is not uncommon, in young children like that. They either do not wipe well or they do not wipe at all... or, they get a little pee on their underwear because they hold it too long or wait until the very last minute to go pee and then a few dribbles gets on their underwear and it gets wet.
To me, her hand washing frequency is not only because she goes to the bathroom often. Because, you said she washes her hands "way too many times a day...." and to me, she does this even if she is not going pee. But washing her hands at other times too, not only when she is going to the bathroom?
Or, is she saying she has to pee so frequently.... but it is to actually wash her hands a lot?
I just don't see how, while she is in school during the week, that she is going to the bathroom that much & frequently, plus having to wash her hands that frequently. Because if she was, wouldn't the Teacher say something? As well.
Also, it could be that it is that particular "highly scented hand sanitizer...." that you said she has been using lately, that has triggered and caused... her red dried out chapped hands. Lately.
So throw that away. Tell her don't use that anymore.