In my honest and humble opinion... the fact that he has lied to her is the biggest red flag. He needs to come clean to her about that before anything goes any further. If she's going to be around she needs to know the honest truth first.
Maybe he was feeling neglected-- that is no excuse. That is something he needed to communicate to YOU, and deal with. And now that you know, it's something the two of you need to work out.
I'd say no to the meeting family and running away in NRE until she has an honest view of your marraige, and understands what's going on first. One missed family dinner isn't a big deal, but all three of you sitting down and making sure things are clear IS.