Gotta love this show. We can't turn against each other! Let's divide into teams and play softball.
There's ways to go about sneaking around in a village, and I'm pretty sure that wasn't it. Our intrepid heroes sneak in, nearly get killed, sneak in again, and only got out because Cool Priestess Lady let them go. And then they get back, and SEAL Doctor has question, but that can wait, since Eve and Levi need to talk about their relationship.
As for Gavin and Izzy, they sort of wrote themselves into a corner here. If he leaves his daughter alone in the modern world or takes her with h