If I am under the IRS federal tax compliance program and my employer has to show me as "Single with 1" dependant, then is that how I have to claim on my taxes?

I gather that your employer received a Lock In Letter from the IRS.  If the IRS believes an employee has consistently submitted incorrect W-4 Forms, they are required to have more taxes withheld on future paychecks.

But you (and your wife) claim on your W-4 with your employer is only for withholding purposes.  You still file a Married Joint tax return.

No, if you are married you must file married- jointly or separate (unless Head of Household applies).  The employer designation of Single, 1 dependent is for withholding taxes from your paycheck not filing the tax return.

The W-4 is only used to determine your withholding. It has nothing to do with your actual tax return. You must file your actual tax return according to your actual marital and dependent information.