Because it's not about bathing suits, towels, or laundry. It's not about your SD, you, or your DH, either. It's about power or control, and her sense that she's lacking some. Because I mean, really, would anyone ever bicker about something as trivial about suits and towels if there wasn't something under it?
If you're going out to get quarters to use a public washing machine, you're already doing way more than I would do. I used to stress about always sending DSS home with his clothes washed on visitation week ends. (It was "mandated" from his mom that he return home in the clothes he arrived in, rather than a sub-par change of clothing from our home.) Often that meant doing laundy even if we didn't have a full load just to wash a pair of jeans.
Truly, who cares if he wears the same pair of pants two days in a row. When my DD was a newborn, I was wearing the same pair of sweatpants day and night for a while! You didn't do anything wrong.