Unfortunately it appears you are on the hook for paying tax on the entire capital gain.
From a tax point of view, you gifted money to your Mom and she used it to pay the property tax, and she took the deduction. An owner or an equitable owner would have paid the tax directly (and taken the deduction). So it's going to be very difficult for you to prove equitable ownership.
Also, your reason for selling ("I would really like to sell and use the equity for a down payment on a new house") does not qualify you for a partial capital gains exclusion.
You may want to consult a local tax attorney, but it appears you do not meet the IRS ownership criteria either as an actual or an equitable owner, nor do you qualify for any of the allowed partial exclusions.