There's your answer to the issue, she specializes in a set of skills that includes tracking. That is how she finds you. She isn't really trying to infiltrate, also infiltration is a general skill expected of a shinobi in the first place. It has been shown in canon that even the mighty Byakugan has its weakness. Also, she is a well known and trusted shinobi within the village due to her role in its intelligence service, meaning she is expected to be one of if not THE most loyal shinobi in the village aside from her superiors as she is trusted with extremely sensitive and potentially village dooming information and tasks, so she may have permission to enter as certain other outsider shinobi do. In canon, we don't really see a whole lot of te Hyuga estate being guarded so closely that the guards ask for your reason or whatever clearance they request. Boruto, yes I'm going there, walks right in when going to Hanabi to test him for the Byakugan. Speaking of which, now that my curiosity is piqued, speedapple, is Hanabi going to be included at any point? She does show up during the Chuunin exams as a spectator, so she would fit in arc 1, though her addition at that point would be risky due to age at the time and her appearance not lending itself to making her older for the sake of not having a potentially Patreon dooming appearance. She appears in Shippuden as well, so arc 2 is possible, but also risky there as I do believe she is under 18 at the time of Shippuden and doesn't look that much older than her original appearance. Her safest appearance, due to the art style of the game being so close to the actual series, would be the Boruto era, where she is in her early 20s and actually looks passable as an adult. Just thinking ahead before the issue of her age and less than adult appearance in certain eras comes up.I'm not underestimating a Jounin, I know what they're capable of but it also needs to be taken into account that she is not a fully fledged one she is a Special Jounin (Tokubetsu Jounin) That means that she was given that title due to her abilities in one field, in her case interrogation gathering from prisoners "torture" and tracking, Orochimaru got an interest in her yeah, but infiltration was never stated as one of her strong suits.
But that is not here or there, she is infiltrating the Hyuga state, a place that only the Hokage should be able to force him/herself w/o permission, full of people with the Byakugan the "All Seeing Eye" that should be able to see through any jutsu that she might use, that should have not been possible under the grounds that she is breaking and entering a clan state, she is dooming herself just by taking that risk. And you mean to tell me that after what happened with Hinata when she was little there are no guards roaming around that should've at least caught her chasing the MC out as that was not a subtle exit, remember that we are allowed to be there as Hinata's sparring partner, she needs a reason to be there, it would have made more sense for here to ambush us right after we leave the state, I mean she can't use Hinata she is already on control 5 so she is NOT going to betray us, Anko at least knows that much or else we would be under her mercy in the TI right know with Tsunade watching with a bowl of popcorn.
Anyways my main complaint is not that she caught us is where she caught us that does not make sense, Another thing is that we must remember that while good the general Jounin is not that big of a deal unless we are talking ROOT or ANBU, most Jounins are portrayed more as cannon fodder to let people like Kakashi, Guy & Asuma and even Kurenai to take care of the real threats, this is because the badass Jounins that you see out there grew up and were active during the 3rd shinobi war meaning you either "GIT GUD" or you die, most Jounins in Naruto's time got the rank during the times of peace and were not that good due to lack of need. BTW the Special Jounin part I got it from the Narutopedia.