Oh, I don't want to even add this. I have a 14 yr old Aussie mix. She did that until probably she was about 6 or 7 ys old, and then just stopped. Why she just kind of stopped then, I don't know.
Do really work hard at making greetings very low-key - when people come over, no dog involvement, no hovering over the cute puppy, no cute puppy/baby talk, nothing. Yep, no touch, no talk, no eye contact. Especially hard with a puppy. Make sure people just ignore her til it's obvious she's comfortable, for however long that takes. And if she does pee, just clean it up. The one thing you don't want to do is make her feel the least bit uncomfortable for peeing. She's not eliminating, as in, having to use the bathroom. She's peeing out of fear - huge difference. No comments, big sighs, ugly faces, etc, on your part. She picks up on that, and knows she's done wrong. The problem gets worse. We kept an easily washable rug right by the front door, as no matter who came over, how they entered, etc, that's where 'it' happened. Easy to soak up with a little towel, and launder as necessary. She never had accidents in the house, used a doggie door, etc, so never had a worry there. It was 100% related to that dreaded front door, entry hall area. Make entries/visitors not involve her at all. Walk right past her, just totally ignore her, keep voices low/soft/normal if possible. Let her figure out that people mean no harm to her, they're nothing to be scared of, all's good. When she's finally comfortable and ready for pets (as in, hopefully now she's seeking them), ask people to pet her under her neck, chest area, talking softly, again, not hovering over her, and not staring into her eyes. Hopefully, it will all start making sense to her. Remember she's still a baby, trying to figure out this human world. Some dogs can barrel into it with no problem, others are more timid.
My girl's great now, no problem at all. Not sure exactly when or why it quit, we suddenly realized she wasn't doing it anymore - and were so happy! After so many years, we were amazed and resigned to her doing it forever. Hang in there, there is hope. If my girl can clear this hurdle, I bet your little Kai can too. And I bet she doesn't do it for years and years, only months (altho I know it seems like an eternity, believe me!). Be patient, go slow, she has so much growing up to do, she'll be a big beautiful strong girl in no time!