She get doubtful at times but mostly dismiss it as his melodrama, if Azula had really been convinced Zuko was bulshitting, she'd have used it, even if at that point she was pretty chill with him (the novelisation has her be actualy serious about restoring Zuko and the whole team up thing, that wasn't a trick, though one of the staff guy said on twitter that they weren't really sure themself on that so we got a few mixed signal in that storyline, take that as you will, i personaly don't put much stock in twitter info but it does fit), it's pretty obvious, Azula always used everything at her disposal.
She isn't weak but she isn't as strong or all-knowing as she try to portray herself to others and her reading people only extent to fear except for Zuko who she can actualy play like a fiddle most of the time (the only time she miss something about him is while he was acting uncharacteristicly dishonorably due to his internal conflict and that was after 3 years without seeing him, that's damn impressive), that was kinda the point of the 'i love him more than i fear you' scene (a scene that the comics ruined, with Mai breaking up with Zuko over the stupidiest shit like they are freaking Ross and Rachel and falling for the first obvious honey trap that came around).
Also her fooling Toph is because Azula always lie, as Zuko said (which only he seems to have realised), she lie even to herself almost constantly so obviously there wouldn't be a difference between when she lie or not.
IMO, that's the irony of the character, she give that aura of power and authority and technicaly even really has it but end up really being just a puppet for Ozai until her breakdown, everything she did and gain, she always immediatly gave to her father after all (which she probably realised, which is why she barely even acknowledge he exist in the comics and is more focused on Zuko and Ursa.)