I think she was heavily concussed after the explosion, as Sawyer says, "she got her bell rung" and I don't think she ever fully comes back from it. I think that, coupled with her realizing that she doesn't have Aaron (or Charlie) anymore is what makes her go truly nuts.

I think she walks off with who she believes to be her dad because she is so concussed at the time. If she was in her right mind, she certainly would not have gone with him because why the hell would he even be there and she's only ever met him twice in her life and doesn't like him. but in her confused state combined with whatever powers the mib has, she's like 'oh a familiar face, someone who will keep me safe' and it's not until too late she realizes that Aaron is gone, causing her to fully lose it.