Your attorney will need to know more about your specific plans, but in general as long as you don't use material from the movies (title, major plot elements, character names, images, sounds, etc) you can be inspired all you want. So "Tiny Thief Thwarter--The Game" is more likely to fly than "Home Alone--The Game", and if TTT weren't named Kevin and was defending a meth lab or a palace instead of a house in Evanston you'd give the Home Alone guys less and less to be quarrelsome about.

Now, you specifically mention "parody" and "fair use," do you intend to quote parts of the movies, or actually parody part of it? Based on your short question I don't really get the sense that's your angle. I more get the sense that you're looking for a new scenario inspired by those movies, and I'd encourage you to use the inspiration to drive toward the new idea rather than attempt a parody of the old.

And good on you for not having it be zombies!