Baby is Mikhail's Aneri and a part of him can't accept that yet. That's why he is hellbent on driving that point home and proving it time and time again to himself.
When he approached her at the Shack last night knowing her family was all there and called her Vicky, he needed to know how she would react. Because Aneri has the same problems. Because somewhere in his mind, she's Aneri.
Notice how he calls her Vicky and not Baby, even though he knows that's her name? Notice how he says hi to her twice waiting for her to react and/or acknowledge him?
He needs to know who Baby would pick in that moment, because his Aneri needs to make those choices too. It's a test to see just how much she is like the Aneri he imagines in real life.
Poor Baby, she's become the axis of Mikhail's dream without even realising it and it's going to cost her dearly and change her carefully planned life for good now.
I feel for her. I really do.