What is a "two-by-four"? What gives Tom the sense that he is in a "two-by-four" situation?

A two-by-four is a board used in construction. In this context, Tom knows he plays a viable role in holding the family together, just as a two-by-four reinforces what's been built. He feels as if he's nailed into a situation he cannot get out of, and that if he leaves, all else will come crashing down.