I know it ought to go without saying, but I'm gonna say it anyway, just to be clear.
While visiting your relatives, do not make the gun "accessible" to you, or them. Doing so would remove the protection of the law from you.
In other words, if you don't have the FOID, don't open the case while in IL.
I'm sure you understood that, but just in case you didn't, now you do.
All else being equal (and it almost never is) bigger bullets tend to work better.