Your guardian could prove this with statements you or your boyfriend have made to her, photos, video or any other evidence. It sounds like it's time for you and your mother to sit down and talk. Perhaps your mother doesn't trust your boyfriend because she doesn't know him. Express your feelings to her for this young man. Then you and this young man should both sit down and talk with your mother.
Communication is key.
I am firmly convinced that many accidents occur because people talk on their car phones. I personally know people who own car phones who have said that they've missed a stop sign or red light because they were wrapped up in a conversation. These people always say they have sworn off using the phone when driving, but you have to wonder if they can stick to their guns. I've stopped many people who were not paying attention to their driving because they were talking on the phone, and I've worked accidents that were a result of this behavior. But the only thing that's going to stop some people from using car phones is being involved in an accident.