Did you every receive the excess money back from your ex spouse? Are you still making alimony payments to her?
From what you have told me it sounds like you have been overstating your deductions by approximately $12,000 per year. If your marginal tax bracket (your top tax bracket) is 35%, then you may be liable for as much as an additional $4200 in taxes for one year. Keep in mind that you will have to do an amended return for each year that was filed incorrectly, so the actual tax may vary from year to year depending on what your top bracket was in that year and what the tax rates were at that time.
In addition to whatever additional tax is owed, the IRS may impose a penalty for late payment which is currently assessed at 0.5% per month on the tax amount due, or a maximum of 25% of the total tax due. There will also be interest compounded daily on the tax that was underpaid. The interest rate used changes quarterly, and is currently at 5%. So as you can see, the amount you may end up owing could be substantial, particularly depending on how many years you need to amend.
In some circumstances, penalties can be waived if the taxpayer can prove that there was reasonable cause for the error. In determining whether or not the IRS will waive penalties, they will generally look at things such as the reason for the error, the taxpayer's previous history of compliance, the length of time it took to report the error and whether or not the circumstances were beyond the taxpayer's control. To apply for a waiver of penalties you would need to submit Form 2210 to the IRS.
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Thank you and good luck in getting this resolved.