The last thing I wanted to have happen was for some to become upset and for cold feelings to come within us and ruin our will to cooperate.
Is the second "for", before "cold", required?
By having the 'for' after 'and', it's saying there were two things the writer wanted not to happen. Without saying 'for', it might convey to the reader that both upset and cold are adjectives for 'feelings'.
The last thing I wanted to have happen was for some to become upset and cold feelings to come within us and ruin our will to cooperate.
To be fair, doing this also makes it sound somewhat weird to an English reader, especially 'to come' coming just after 'to become'.
So yes, I guess the 'for' in the word does matter in this instance in order to ensure the reader interprets it correctly.
I hope I managed to answer?
You don’t need the second for. As long as the preposition works with each element, there’s no need to repeat it.
Also, you should replace within with between.