Hi, Annalee. Probably there are not enough carbs in a stick of gum or a couple of tic-tacs to make a big difference in the child's blood sugar levels. Other candies contain more carbs, so they would probably make a bigger difference.
Have you asked the parents? I wouldn't give her gum or candy without checking with them first. They may object depending on how closely they, or the child, monitor her diet, insulin and blood sugar levels.
There are sugar-free gums. Those would probably be a better choice to give the child than regular gum. The good thing about sugar-free gum is that you can give it to both the child with diabetes and her brother. It's hard for most children to accept being treated differently when they have diabetes. So giving them the same kind of gum (sugar-free) would be best.