So you like to play split-screen games, but Black Ops is one of the glitchiest games ever made, so the hacker in split-screen is buggy like the rest of this game, here is what to do:

Firstly, most things can still be hacked, the words just don't show up, give it a try.

The big issue is the doors, you have hacker out and it just doesn't work on doors: here is the fix:

Stand so the door says '750/1000/1250 to open' then back out of the range of the doors' text. Just as you get out of range, you should be able to hit X with te hacker out and hack the door (it won't say that you can hack it, just try). If you aren't in the right spot at first, move around a little until you get it.