I stayed at Beach Club in summer 2019 and my favorite time to swim was in the evening, after returning from the parks. No sunburns and it was less crowded. The pools were open quite late then - 10 or 11 I believe, and the quiet pool at the Polynesian was open until midnight.
We have our first BC stay coming up in June and appreciate this advice. My girls are all teens so I think we will plan our pool time for after the parks, depending on hours. Then everyone can shower and be ready to hit the ground running in the morning.