Warning: Armchair psychology by non-professional...
Thinking back, Randall also took that "caretaker" role when Jack moved out for a couple of nights. Kevin even called him out on it. It's not remotely Oedipal from a sexual perspective. I think Rebecca just was idolized and Randall picked a side rather quickly. SO... when Jack died, is part of Randall's guilt the underlying belief that Jack was not as good of a husband as he should have been? Some deep-seeded resentment that Rebecca should have been taken better care for than Randall thought she was? Or that he had wished (secretly) that Jack would leave and she would be happier? It would have been childish and wrong but perhaps there's guilt there because of Jack's untimely death. So he tolerated Miguel originally because he realized he COULDN'T be what his mother needed and Miguel made her happy?
Now add that his "Madonna" had feet of clay and lied to him about something important - that crashed his vision. I honestly believe the 'crime' of not telling him was not a big deal before 18 and after that, there were extenuating circumstances that rocking Randall's world for the next few years would have been debatable. If William had gone back to using, it would have been devastating to feel like he lost a second parent all over again. If William was great, he might leap to him as a father figure and Rebecca would likely resent that immediately post Jack's death. Still, 36 was TOO LATE. Mid-20's would have been better. Once Randall was stable, had a wife and a life and identity that could withstand an impact if William was still using or an asshole. But by then Jack had ALSO risen to sainthood because he died protecting his family. So her 'crime' was against Jack.
Basically -- by not having told Jack, Rebecca cast the die as her role of 'villain'. That was her biggest mistake IMO. Second was not telling Randall after some respectful distance post 18 + Jack's death.
But honestly, Randall's fantasy of a Howard fraternity was also telling. As a black man, raised mostly white, he has shown a constant 'what if' mentality. His career change from money making weather futures expert to councilman shows that he ultimately rejected his chosen path of financial power broker. It didn't have the people element he wanted. So... he had an identity crisis at ~36. And he's nearly 40 and NOT at peace with it. He's not at peace with what he perceived as a selfish withholding of identity data by Rebecca.
BUT... that's still VERY self-centered. Life happened. Those skills he developed as a financial power-broker is WHY he's probably good at councilman from an economics perspective. That's extremely valuable for his community. So.. Randall needs to VALUE the tapestry of his life and look forward. His response to Rebecca's health crisis is him indulging his WORST childish instincts. And he needs to be told "no". Firmly, and with love, but he need to be told "no".
But this is This is Us. And Kevin will have no tolerance for what he already saw as a teenager as an unhealthy predilection to idolize/own his mother. So... that's not going to go well.
Kate's response is probably going to be "what does Mom want" and will side with Kevin.
So... strap in.. it's going to be a bumpy ride.