No, there´s no mate in 2.
Strange eval from chess.com engine
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First of all, where did you get the engine? Or is there any possibility to analyze games on with the engine here?
As second, I'd say you just had a bug going. The engine just worked incorrectly there, and if you get this often, you should probably contact chess.com about it.
And third, not very important: a quick analysis with Houdini 4 shows me that at the second diagram, 34. Rd6 is the best move.
I analyzed a game reasently, using chess.com's engine (says its Elo is ~2500). The game had reached this position, which the engine evaluates as +2.34 i.e. white is better:
Then Black played 32...Ke7 which allows 33.d8=Q#. The strange thing is that Ke7 was rated as a mistake. How is that not a blunder?
White is not exactly a GM, so he overlooked 33.d8=Q#!! and played 33.Rd5 instead, avoiding 33...Kxd6 and Black replied 33...Kf6, reaching this position:
Now, the engine gives this position the eval (Mat02). White is still no GM and plays 34.a4 which receives one questionmark from the engine: "Best move is 34. Ra6 Ra8 35. Rc6 Kf7 36. Rxe5 Nd8 37. Rc3 Ne6" How is this the best continuation for white if the position is in fact Mat02?
I don't see the mate in two; do you?