Sort:  

Thank you for alerting me to the chess engine. The problem is so much easier using it. Now I look forward to solving some more. Yes the rook is the wrong initial move because the queen can capture the rook putting white king in check.

I took a look at the video and I see two variant:
if queen a8 then white queen a6++
if king take pawn first then queen to (b6+, b8++)