How do you address relatives/people that are afraid of talking to you?

How do you address relatives/people that are afraid of talking to you? Talking with others is already hard enough, but quarantine had made my stutter (which is already severe) exponentially worse. I live with some older relatives, and it’s been even more challenging trying to communicate with them. They always seem hopeful when I say fluently say something like “good morning, how are you?”, and then they immediately become apprehensive and look like a deer in headlights because my stutter comes right back out full force. I don’t want to be blunt and accuse them of something like this (I know there’s no malice) but at this point it’s starting to kind of eat away at me :(