HI! Should me and my wife file married but separate so that my ex wife won't get her money for the back child support that I owe

By filing separate returns, you do not get many credits and deductions.

You can file Form 8379 (Injured Spouse) with your joint tax return. The IRS will allocate the refund between you and your spouse. But by filing Form 8379, your refund will be delayed by about 2 months.

You can file as married filing jointly (MFJ) or married filing separately. In most cases, it is better to file as MFJ. Read Your U.S. Tax Return: Filing Status for Married