I've no idea what's going on now... I was able to get caught peeping the girls at the swimming pool on v0.2 and now I just peep on them never being caught. I can't start the story line with Kate this way. Am I missing something?
I was also stuck on this for the longest time and couldn't figure out how to start the swim club questline until I stumbled upon Nina outside the pool. If you're in the same situation I was, then you have to:
1. Talk to Nina when she's out of the pool at 17:00. Answer that "you love swimming" and she'll try to get you on the team. She says to come at 13:00 tomorrow to see what they say.
2. Go to the pool at 13:00 and try to enter. She'll say that they're still working it out.
3. After this, you need to peak on Nina showering at 13:00 by the bushes on the right and hit "keep watching". There's a chance that you'll hear footsteps and need to hide (If it ends with "leave" then try again the next day).
4. Choose "the tree" and you'll get caught. Repeat the process another day and get caught a second time.
5. Now when you try to enter the pool at 13:00 you can join the club.
6. Clean the pool with the broom northeast of the pool up to twice a day to increase affection with the club and unlock their scenes.
Hope this helps!