I am taking a job that is over 100 miles from my home (where my wife and 2 kids live). I don't want to relocate, or displace them from a great school district. To take this job, which is not commutable distance, I plan to rent an apartment close to work for the week, and commute between that apartment and my house only on weekends. Besides the unfortunate nature of the situation, is there any tax benefit here? Can I deduct the rent from my taxes?

No, you can't deduct the rent - sorry. Nor can you deduct the cost of traveling between your home and the new job location. I am assuming here that you are an employee of this company (not an independent contractor), that the office in the city 100 miles away is your primary office, and that this isn't some sort of temporary assignment by your empoyer.

Here is a link to the IRS web site that gives info on deducting costs as an employee:

Tax Topics - Topic 514 Employee Business Expenses

Agreed! If the job was temporary (less than a year), then apartmet rent and other per diem costs MAY be deductible, providing you met certain criteria.

However, based on your posting, you are out of luck!