2. Bd2 Rf1+ 3. Be1
Should keep white going. Black will win a pawn by Rxh2, and Bf2 (threatening the pinned bishop) just loses the pinning rook. I think by playing Bd2 and Be1 should give fair drawing chances (if not winning chances) because of whites passed pawn. Correct me if I'm wrong, I am after all, a novice.
Almost everyone knows how to stack up the Rooks or Queen\Rooks to attack the back rank. The problem I see is if your opponent have attackers on the back rank it confuses people. After you run through the attack sequence in your head you realize you don't have enough power to mate.
So how can we stop the white rook on h1 from interposing. You don't need to take it, you just need to slow it down by interposing one of your pieces.
White have a lot of options to stop the mate. He could have moves his bishop so the king could move. He could have taken the Black bishop and lost his rook. The lesson here is if you are in an attacking position ask yourself what pieces are stopping the mate. If you can't take it, block it.