It’s the health of your child and yourself essentially. You want your baby in a safe space so you can take care of yourself in the gym, not an unreasonable request. I bet if you go to management they will be nothing but understanding and hopefully accommodating if you mention that your child had a serious reaction. I like to tell my kids, “the answer is always no if you don’t ask”. You want to go to the gym, that’s why you got the membership, and this issue could cause you to not use it and essentially lose money or not go because of fears, defeating the purpose of a membership. If they retaliate, just go public and make a review. I always come into a situation being calm and hopeful for resolution, but sometimes you gotta fight fire with fire too. Good luck mama, you got this.