If I had a "hypothetical" situation where 2 stocks correlated well in a 1:2 movement together, I would take something akin to a 2:1 long/short equity pair (so expected movement of 2% vs 2%) and do what I do in my pairs trading --- try to trade the trend as well as take advantage of the intraday fluctuatiions in the spread difference b/t the two underkyings (not the B/A spread). IOW, if the trend is up in the AM, add more to the long side or reduce the short side. If the trend is down, do the opposite. The success of this is totally dependent on your ability to read the trend as well as the reversals. Where this can get really entertaining is if you can find more than 2 components that correlate. If so, then whatever the move, in whatever the direction provides a nice gain on one side and a "similar" loss on the other. In addition to the aforementioned intraday bias shift, you have a second game within the game. You can take profits on the winning side and substitute the add'l component, restoring the pair. IOW, start long A and short B. They both move up. Sell A to close, book the profit and buy C. Your pair is now short B and long C. You haven't made a profit but you've booked gains while holding paper losses. As fluctuations and reversals occur b/t components, hopefully you're booking profits and recouping paper losses. You'd be surprised at what can be done if you find the right correlation. I feel like I'm tring to force a round peg into a square hole since the actual trading of a pair is far more complex and you have presented only minimal information in re a 2:1 movement. So take it with a grain of salt. This concept may not suit you at all..
Unfortunately, there are two indicators called relative strength (at least in the old software packages). The better known one is Welles Wilder's baby (RSI). Comparative Relative Strength is simply dividing the closes of stock A by stock B. If the graph of this is rising, stock A is stroner. If declining, stock B.