Of course you should invite her out... just like you'd invite a friend. If she can make it great, if she can't that's okay too... wait two weeks and invite her again. Eventually she may start inviting you! That's kind of how it happened with my husband. The babysteps of friendship. Gosh, and you're not even in divorce.
I might be wrong here, but I think your wife is feeling a lot of guilt. I also think with OM out of town it's like a detox situation. He was like a drug and she's going through withdraw... that's just my guess.
There is no arriving, ever. It is all a continual becoming.