I was wondering the same thing, how could Claire and Moira know each other and/or why are they in this together, but then several possibilities came to my mind, all of which stem from the fact that we have little to no information regarding what Claire and Barry (and by extension, his daughters) have been up to since Raccoon City. Here's a couple of ideas:
1) Moira is another member of TerraSave. This in turn would pave the way for several possibilities; for example, either TerraSave is the target of a conspiracy and whoever is behind it kidnaps its agents on purpose, or TerraSave itself is evil and Claire and Moira know too much.
2) Chris is the target, and kidnapping his sister and the daughter of his former best friend (and who knows whoever else) is a way to lure him into a trap. The one behind this is likely someone who has a personal history with him, like Jessica, and it would make sense to make her the main villain because this game is a continuation of Revelations, but since Capcom stated that Chris won't appear, it's rather unlikely.
3) Moira is secretly the villain, and the abduction of Claire and the events afterwards, while seemingly random, have been carefully orchestrated to reach a specific goal. This is a Revelations game after all, and considering its predecessor and what we've already been told about it being full of twists and secrets and all that, it's possible.
4) The connection is Sherry, who lived in the same place and went to the same school as one, if not both of Barry's daughters. The RE universe is a small one, after all. Moira looks at least five years younger than Sherry, so they probably weren't classmates, but we don't know who is who in Barry's family photo, so she might be the smaller one while her older sister (Polly) was Sherry's friend and/or classmate.
5) For all we know, Claire could even have been friends with Barry and babysitting his daughters when they were younger.
6) Claire and Moira don't know each other at all, but meet by chance. Except for games that begin as BSAA missions, that is usually the case in RE.
As for the rest, about the story and timeline placement and all that, we just have to wait. We usually don't learn a lot about these things before the game comes out anyway.