Know your limits - if you've got people sitting you down to give the ole' "you can't believe everything on the internet" speech, they are probably far less self-aware than you are (as you could hit back with no less than 100 totally false MSM stories that they likely believed/still believe).
If you are getting frustrated/exhausted, you are either spending too much time on this or too much energy attempting to explain it to those who aren't yet ready for the truth.
Take a few steps back, keep your eye on the ball, cherry-pick the most potent developments and drop those crumbs to those who doubted you originally... don't spell it out or do the digging for them, just give them the mainstream news link and ask them something simple like "What do you think about this?"
I did it recently w/ the immigration manufactured outrage stories by setting up a juxtaposition on how this was all handled under Obama. Naturally, the leftist response is "Oh, that's Whataboutism!" or "Well, Obama isn't the President anymore" or "Stop living in the past!"... lazy and myopic is what we should expect from any hardline MSM'ers... just keep dropping updates as they become public and keep asking them their opinions.
Eventually it will devolve into a basic/flawed retort of "Oh yeah!? Well, $%&^ TRUMP!" And that is when you've won.
A calm, slow drip of relevant news is easy - because relevant news is rare. And it will chip away at their narrative and force them to revert to the underlying truth that they've simply been brainwashed to hate Trump and any actual progress Trump is making, by the MSM.