What is a succinct latin translation for "Your hatred makes us
stronger" or a paraphrase of the same?

Hi mddg-ga -

"Your hatred makes us stronger" translates as follows:

                Odium vestrum nos corroborat   [plural you]   OR

                Odium tuum nos corroborat      [singular you] 

Vocabulary links:

odium
http://catholic.archives.nd.edu/cgi-bin/lookdown.pl?odium

corroborare
http://catholic.archives.nd.edu/cgi-bin/words.exe?corroborare

You might also be interested in this:

Latin phrases used in English
http://www.math.ohio-state.edu/~econrad/lang/lphrase.html

All the best,

alanna-ga

As a purely prosaic translation, I might suggest:

Vestrum odium nos auget.

(Where the "your" is plural...)

Not sure if that's quite correct, but it's a very basic start...