It's definitely all about your tone and demeanor. Going from your post and her reaction to you, you did it the right way. People who stutter can often see a person's displeasure or helpfulness towards them almost in an instant as soon as they have a block. (Speaking from experience) I've had conversations with my friends to tell them to usually let me finish out my sentence because at that point if I don't have the chance to finish then why say anything in the first place! It depends on the substance of what I'm saying. If it's a simple ask of petting someone's pet it's not a big deal. Once someone with a stutter has that sigh of relief like you explained from that woman, we usually have way better fluency for the rest of the conversation. It's all about the way we think you are perceiving us! Thank you for posting this! God Bless