I'm not sure about the inflatable bathing suit, but when my DD was 4, she wore the arm floaties all day and no one stopped us.
Also, when it comes to the shoes, I would buy your child actual water shoes and those can stay on for all the slides. The only time you have to remove them is for Summit Plummit which is something your child won't be doing anyway.
I would also recommend the water shoes for you because then you don't have to worry about walking around with bare feet.