This makes no sense. If you're going to cover up vaccination side effects with a huge conspiracy, why choose child abuse and mystery death? There are no vaccination for those.
Wouldn't it make more sense, and be more efficient, to tie the deaths to something that requires vaccination? Say the babies died of Whooping Farts or Plaid Fever or the Gizmonic Plague? THEN you can drive fearful parents into doctor offices to further vaccinations, to make sure they're up-to-date. More bang for your buck.
And how would you choose between the two conditions for a conspiracy? Shaken Baby leads to prosecution. So now you're not only faking the diagnosis, but you have to fake the evidence to prosecute a parent who was already behaving the way you wanted them to, they had the kid vaccinated. But SIDS, no one gets punished. It's tragic, and sad, but these things happen.
So how do you choose who gets the 'child abuse' fake death and who gets the 'act of god' fake death? And why choose ANY parents for prosecution? Why tie up the courts with fake Shaken Baby when what they really want is to prosecute the anti-vaxxers for child endangerment?
THis is really a vile, die-in-a-fire sort of conspiracy theory, but it really needs a lot more thought put into it, it just doesn't fit together at all.