If Germany foregoes rocketry research during the 1930s and 40s...

...what would happen (a) to the German war effort, and (b) how much longer would it take to achieve space flight? For specifics, the point of divergence is 11 December 1937, when an errant A3 launch kills Von Braun and Dornberger but leaves Walter Thiel alive.
 
...what would happen (a) to the German war effort,

It arguably performs better given the massive amount of resources that went into the V-2 program. For comparison purposes, it was about 50% more expensive than the Manhattan Project and was on par with the entire B-29 project's cost while having no real impact on the course of the war.

and (b) how much longer would it take to achieve space flight? For specifics, the point of divergence is 11 December 1937, when an errant A3 launch kills Von Braun and Dornberger but leaves Walter Thiel alive.

About the same length of time.
 
The Death of Von Braun would put R&D on rockets on complete different way
instead liquid fuel rocket, the Germans would go for Herman Oberth proposal large solid rocket engine.
but the Death of project Manager Dornberger would delay the program considerably
 
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