I see no useful guidelines on which way to extend from the crosscut, when to atari/extend, or when to double atari/extend. This may be useful in this discussion.

Usually, extending the stone you can least afford to lose, is a good strategy. The stone you want to lose least is the center stone, because its loss would have an impact on the whole board while losing the stone in the corner only has a local impact. - The Magic of Go

Two good reference articles on cross-cuts: http://shinbo.free.fr/TheMagicOfGo/index.php?tmog=251 http://shinbo.free.fr/TheMagicOfGo/index.php?tmog=252

Perhaps then we can discuss, in general terms, the circumstances where you want to:

1) extend 2) Atari, then extend 3) Double Atari, then extend

It sometimes helps people to see clear-cut examples of when you should do something right as opposed to when you really do not have a clear choice and you try to explain away a hair's difference. Such is Go, and Chess. So I would propose, based on your comments, to elaborate on:

a) when to extend from the weaker stone b) when to extend from the center stone

and when to:

a) atari/extend from the weaker stone b) atari/extend from the center stone

and, if possible, do the same for the double atari/extension as well. The big caveat would be that these are simply guidelines/first inclinations, and not written in stone.