I have attempted to attach your link discussing how Irina’s death at the hands of Caius was unjust (hopefully the summary helps if it hasn’t worked).
Irina obviously was caught up in horror over the presumed immortal child- but if Aro read her mind (a reasonable assumption?) then how would he not have caught the extraneous sensory detail of a sounding heartbeat do you think? Or is it more Irina genuinely didn’t register it despite vampire senses? (Or Aro didn’t check with his gift?)
Just thought it’d be interesting to see your thoughts on logistics over that aspect.
My post discussing Irina's death.
The reason why I think Irina's death was unjust was she acted in good faith, and had no organic venue of finding out she was wrong. She fully believed Renesmee was an immortal child, she had no reason not to and it was smart of her to run when Bella spotted her rather than risk getting in a fight with a newborn vampire.
She clearly hadn't registered Renesmee having a heartbeat, and if she heard something then at a distance, given the vampiric appearance and behavior she had just witnessed, and Renesmee's heartbeat being so much faster than a human's, Irina would have been reasonable in assuming it was some other animal's heartbeat she was hearing or something else entirely.
The only way she had of finding out Renesmee wasn't an immortal child was by approaching the Cullens, which would be a death sentence as Alice and Edward would know she wasn't going to cover for them (and what is there to approach them about? They've made an immortal child, "Thought I'd say hi before telling Aro. It's been good!"), and even if she had her phone on her (which seems to have been the case, as her sisters tried calling) that's no good once she's entered a body of water, which she would have to to hide her trail and get to Italy (And to my recollection, the Cullens' attempt to stop her ended when her trail did, ergo she did this early).
The only hope here would be if she thought to call her sisters from a payphone to let them know what had happened and not to go near the Cullens, but she clearly didn't do that.
So, Irina is excused in my eyes, and I expect Caius wouldn't have cared if she hadn't made the Volturi look like fools and he didn't want a fight.