“independence from” or “independence to”?

"Independence from."

+1

"independence of": John declares the independence of John Republic.

"independence from": The union, though weak and poor, managed to remain their independence from other big, influential interest groups.

Can you sense the difference there?

Regarding: "The union, though weak and poor, managed to remain their independence from other big, influential interest groups."

This isn't quite right. I would suggest that it should be either "...maintained their independence from..." or "...remained independent from..."

Oops, wrong tense. That's ...maintain...remain..., no "-ed" at the end.

1) Argentina gained independence from Spain in 1816. (New Oxford American Dictionary, 2nd Edition. © 2005 by Oxford University Press, Inc.)

2) independence of irrelevant alternatives; independence of random variables

independence FROM {named object}
independence OF {subject}, no named object that subject is independent from; general idea of independence meant.
Or as the irregular verb bashers would have it, "meaned." (joke)

also
The union, though weak and poor, managed to remain their

1- remain may be a typo for RETAIN?
2- THEIR is not allowable here since it is not the union and something else, e.g. the army. Therefore THEIR must be ITS to match the singular subject.