How is this different than [[Dualcaster Mage]] being targeted with [[Heat Shimmer]] off of [[Zada, Hedron Grinder]]? The effect you're saying would mean that the initial trigger of Heat shimmer would finish and that Dualcaster Mage would be unable to target the initial Heat Shimmer because it has not finished resolving, correct?

No.

Target Zada w/ Heat Shimmer. Zada's ability goes on the stack. Hold priority.

With Heat Shimmer on the stack (i.e. not resolving yet) flash in Dual Caster Mage and put DCM's ability on the stack.

stack:

• Copy target instant or sorcery (DCM)
• Copy instant or sorcery that only targets zada blablabla (ZHG)
• Heat Shimmer <bottom of stack>

DCM's ability resolves, putting a copy of Heat Shimmer on the stack.

stack:

• Heat Shimmer copy (targeting Zada)
• Zada trigger of Heat Shimmer
• Heat Shimmer (targeting Zada) <bottom of stack>

The copy does not trigger Zada.

You'd create a token copy of Zada from the Heat Shimmer copy and then immediately sack either the original or the token copy to state based actions.

Zada's ability would resolve and you'd put a copy of Heat Shimmer on the stack for each other creature you control.

Those would resolve in any order you chose (you can stack copies that come into existence however you'd like) with any ETB effects resolving before moving to the next HS copy (since each one is discrete).

Eventually you'd resolve the original spell and then sac a Zada to state based actions.

Why are you DCMing the Heat Shimmer, again?