Did they call and make appointments? My wife is under the assumption from the places she's signed up at that they will call her when her name comes up. I feel like you probably need to proactively do this like it sounds like your family members did,
They made the appointments online. They had also been on some of the waiting lists with the county health department and the vaccine clinic coming to the convention center. Down the line as they catch up a bit I think that waiting to be contacted is an option, but for now proactive seems the way to go.