You can use the fact that you are teaching her to pronounce the words she asks for slowly (compared to normal situation when it sounds weird). Also try telling her about your stutter, i have heard this advice a lot and i think it might help you with the people you tutor, it will relieve some of the tension you have trust me. Also i want to tell you that you are so brave to choose to be a teacher while being a stutterer, you are just straight bold.