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:
After killing a zombie by throwing a weapon at it then retrieving it, reloading a checkpoint, dying and respawning, completing an objective, or giving items to Jin to store (taking a weapon out of storage, or traveling to a new area with weapons in her inventory), a weapon(s) might spontaneously delete from the inventory it is located in. Full Inventory's will not drop items from Jin, but delete the item(their are some cases when the item will drop to the floor).
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:
Fixed: disappearing items when there is no place in inventory and a player tries to get an item from Jin’s storage
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.