P.M.
Tough problems, especially when this behavior is interpreted as a lack of respect that makes you feel angry. I'd personally chalk it up to three things; a strong and independent little personality, a need for more sleep, and research into what IS normal for a child his age. (Bud-nipping has its place, but too much 'grafting of expectations' makes for an impossible amount of bud-nipping.)
It sounds like you're doing a lot right, especially considering you have other children to care for. I don't think his behavior is unusual for 2.5. Unfortunately, kids are not little machines with dials we can set to "behave," and every single one is an individual, so the range of "normal" is actually pretty broad.
While learning water safety is a wonderful opportunity, it is apparently not what he'd like to be doing this year. Can you allow him any leeway on that, and perhaps other things that you choose that he'd prefer not to do. You'll simplify your life and his. He will have many opportunities in the future to do things as they become interesting to him. Choose only a few of the most important things to push, like helping him get enough rest. Children's lives tend to be hugely over-controlled in the modern family, and its harder for everybody than it needs to be.
You might want to explore some of the very good, research-supported alternatives to traditional discipline/punishment methods. I have found the approaches taught in Emotion Coaching or empathetic parenting to be wildly effective with my grandson and other littles I've worked with. This is not soft, lenient, or pushover parenting. This is thoughtful, bounded and consistent teaching that can result in calmer, happier families. Google these terms for more if that interests you.