It sounds like both you and your mother have both adopted an epistemology that incorporates the perceived amount of censorship, lies, and coercion performed by proponents of some claim into your discernment of the truth value of that claim. Namely, you both seem to have adopted some level of doubt about pro-vaccine claims because you both perceive that proponents of pro-vaccine claims participate in censorship, lies and coercion, or that those proponents of these claims do not engage in reasonable arguments with their critics.

There are two problems with this type of epistemology. The first is that, like all claims, attributes of the people making the claims are not relevant to the truth value of the claim ("fallacy of irrelevance"). The second is more important and more unique to this particular epistemology: the actions you perceive to be conducted by perceived proponents of some claim will vary heavily based on your own behavior. For instance, how do you know that pro-vaccine people "can't win arguments" and instead "stop them because the other side is too stupid"? Or that there is "massive censorship" favoring the pro-vaccine viewpoint? Surely that is just based on your own "media diet." Surely that perception depends heavily on where you spend your time on Twitter, YouTube, cable news, etc. Would you perceive something differently if it were the case that the vast majority of medical and public health experts who are pro-vaccine in fact have engaged in numerous reasonable arguments with critics and have nonetheless come to the same conclusion? Is there ever a point in which litigation of existing criticisms can end so that we can move on to new criticisms?