It's hard to say that you are wrong to ask your child about when she was sick because she has medical issues that you need to address. And since they are also dietary, you need to know when it happened.
And your ex clearly is in denial or is just trying to make your life more difficult at the expense of your child.
Have you considered modifying the parenting plan where your ex has less time with your child?
If your daughter will tell a GAL or the judge what she tells you about when she gets sick, and especially if it contradicts when your ex says she gets sick, that will help you.
Unfortunately, it will put your daughter in the middle. Sometimes that is unavoidable. Your daughter's health is more important. And all of the turmoil that your ex is creating isn't helping at all.