Swimming is great but changing is awful!
Plan your locker bags. You'll probably be holding a wet grumpy toddler when you get out, you want towels on top in the locker so you can grab them easily, a bag for wet stuff, a bag with your clothes. You can leave shoes and coats in the locker and relock it then get them when you're dressed. Put things in the locker in the right order.
Swimming makes them tired and hungry so have a snack with you and don't plan anything too energetic straight after. Half hour to three quarters of an hour is usually long enough. Watch out for their lips going a bit purple, it means they're child and ready to get out (or at least need to be encouraged to move more!)
I take armbands. Bath toys are also fun, anything that floats or cups or mini watering can etc. Just one or two or you'll be fending off all the other toddlers!
As well as swirling around you can get them to sit on the edge then fall forward into your arms, lower their mouth in the water to blow bubbles, practise kicking legs etc
Yes to reusing swim nappies. Places can be weird about the actual reusable ones but they won't know what you've got on under a suit.
Being wet and drippy in a confined space getting dressed after is one of my least favourite things, I remember a time DD kept trying to latch on to my boobs every time I bent down to sort her out! Wrap them in a towel then dry yourself as a priority, or you will drip on them.
Also be prepared for your kid to hate it at least at first, both of mine went recently after a long hiatus and the sound and splashing made them both a bit scared to begin with.