She was first shown early in the first season, with Phillip using her to spy for him on her husband, who works for the Department of Defense, and his colleagues; Phillip is pretending to working for the Swedish government, and she's talks about how she's in love with him. Phillip tells Elizabeth that Analise isn't cut out for spy work.

Last season, they showed Phillip getting her to hook up with the ISI guy. And I'm pretty sure she got pissed off at Phillip for trying to turn her "into a whore" or something along those lines. Which would give another bit of depth with her ending up falling for the ISI guy.

>Was the "uncle" they had lunch with their new handler from the
>center?

He was. He was also their "old" handler before character actress Margo Martindale. They complained about his absence season #1 when they first met her.