Peter,
the rule seems to be written specifically for the plays at home - squeeze play. If R3 gets tagged out, then no interference. If R3 does not get tagged out and the umpire feels it is due to the batter, then the batter is called out and R3 is returned to 3rd.
Now you are applying the rule to a double steal attempt of 2nd and home. First of all, I've seen very few catchers confident enough that they could throw to 2nd tag an out and still hold the runner at 3rd - completely independent of batter interference. Most I have seen just accept that the runner is going to advance to 2nd and hold the ball to prevent R3 from coming home.
I think the catcher is also accepting that to make a throw to 2nd also means R3 is going to score... to make that throw is likey the wrong thing to do, period - again, completely independent of batter interference.
Now you have posed a throw to second with slight batter interference and not enough interference to prevent the put-out at 2nd. Therefore out at 2nd stands and R3 advances home for score. I think just having the catcher make that throw to second and expecting that the defense will also be able to hold R3 is probably unreasonable on the catcher's part. The pitcher may be capable of holding R1 & R3 but I don't think the catcher can as readily hold both.
I don't think the rule needs changed - catcher just shouldn't make that throw.
JMO
