I can give her my weapons easily but when I try to take them back and click on them they disappear and are gone for good. Is this a glitch, has anyone had the same problem? Thanks for your answers in advance!
As it turns out, your suspicion may be correct. The Dead Island wiki lists this as a glitch - the emphasis is mine:
But hey! There's good news! Well, sort of. In October, they released a patch for the PC version that fixed this issue among others:
Unfortunately, the update for the 360 that was released in November was supposed to contain the same set of fixes, as well as other improvements (including boosting the level cap to 60) ... and it did not list a fix for the issue you describe.
I see no recent news about another patch, just about DLC, so for the time being, this is a bug, and the only workaround is to remember to check your inventory every time you interact with Jin.