I am hearing you and picking up what you are laying down. You and I seem to be looking at this from a long view and what the attorneys for both sides are going to do with this evidence. And I completely believe that recent prior cases in the news about child heat vehicle deaths will be featured prominently in the defense of these searches in an attempt to make those searches appear more inncocent, the actions of worried first time parents.
But the rest of their web histories should be able to bear that out. For instance, reading several news reports about a specific story and/or commenting on such reports/articles. Researching specific temps in the area where the case occurred and whether those temps and other case info matches up with other facts in that case.
Their searches should be able to tie back to specific questions or concerns in any recent case of heat child death and their history should also show a more than passing interest in that case.
My guess is that the defense will not be able to do that. But ever since the case involving the woman with the name I refuse to speak which involved web searches and the smell of dead bodies I worry about jurors in general.
It's why I am glad none of these things matter based on the charges at hand IMO. They will probably prevent any charges against mom unless some new search shattering evidence comes to light, but for the charges against dad, neither malice nor premeditation factor into his charges so the searches will end up being moot.
I am curious whether those searches will even get big play in the trial. They were needed in order to get the search warrants so LE could look for evidence of premeditation if it exists. But they are not needed to prove the charges at hand and could IMO confuse the issue or muddy the waters for a jury.