hi hairnets
My wife doesn't swim so I always took our 2 girls swimming, from babies up till about age 10. After that they mostly went on their own or with pals (in Edinburgh you have to be age 10 to be allowed to use the pools without an adult accompanying). They're 14 and 15 now.
Granted none of us was claustrophobic (get help now btw), but TBH getting changed was never a big problem, whether it was the local authority pools (cubicles) or my own health club at the time (open changing area) I always managed to work something out. By that I mean they got changed in a cubicle with me, or in a corner/round a corner in the open areas, with me strategically placed between them and other patrons. or good use of huge towels (well all towels seem huge when you're 5!) etc, a bit like getting changed on the beach. And it certainly was NOT to hide them away from the prying eyes of evil men, it was to avoid other men's embarrasment, and we WERE in the mens changing room.
The oldest did develop an embarrasment of her own, before she was 8, and then used female changing rooms or her own cubilce, never a problem. However, I lost HOURS of my life sitting waiting for the pair of them to exit the female changing rooms, the older they got the longer it appeared to take them to get ready 
For me , reading your OP, the worst thing is your ex shouting at her in public. It's more likely to put her off going swimming than solve anything.