your plan looks great on paper (well, on screen!), but the practicalities of mixing beach with urban night-time activities without a break are troublesome.
A beach is a beach, and I hope you'll have plenty more opportunities to walk on sand and wade into the sea elsewhere - but I'd suggest on your day-trip you concentrate on sight-seeing and people-watching.
A hotel pool would give the opportunity to swim AND freshen up - but i have no idea how easy it is to blag entrance, or how cheap it is to enter as pool guest. You could try going to a pool bar for a drink, and taking it from there: I've certainly been up to the (tiny) Ipanema Plaza pool bar, and to the (ex)-Intercontinental one without being challenged. As for public pools I don't even know if these exist.