If you did not live in the home as your personal home for at least 2 years prior to the sale and own it for those two years, then you owe capital gains tax on any gain.
This is going to be a pain to figure out. (Gifting a home to a child almost always has unexpected tax consequences and you are trying to build a barn after the horse has run away.) It would have been much simpler and lower tax if your mother had sold the house and gifted you the cash after.
Your gain is the difference between the selling price and your cost basis. It has nothing to do with the amount of cash actually paid out. (You might have a large gain but no money if there was also a large mortgage on the property, for example.)
The sales proceeds are reduced by certain selling expenses including real estate commission, your attorney fees, and any state or county transfer taxes or required inspections that you paid as the seller.
Since the home was a gift, your cost basis is the same as your mother -- she gave you her cost basis when she gave you the home.
Her adjusted cost basis is what she originally paid for the home (possibly many years ago), plus any permanent improvements she paid, plus an adjustment for the death of your father. It's easier to explain by example.
Suppose the home was bought in 1970 by your parents together for $20,000. Then they built an addition for $10,000. The adjusted cost basis is now $30,000 and your mother's half is $15,000. Let's suppose your father died 5 years ago and the house was worth $80,000 at the time. Your mother inherits his share of the house to become sole owner, and she also gains a stepped up cost basis equal to the value of the home at the time of his death. So the cost basis on the half she owned is still $15,000 but the cost basis on the half she inherited is now $40,000 (half the value as of the date your father died.) So her cost basis is now $55,000. She gives you her cost basis when she gave you the house. So you sell it for $90,000, less $6,000 of expenses, for a net selling price of $84,000. You have a capital gain of $29,000 that will be taxed at 15% for long term capital gains.
You need to be very diligent to document the home's cost basis. The price your parents originally paid will be in the county records. Hopefully they have copies of the bills for any remodeling or improvements. The value on the date of your father's death can be determined by a qualified appraiser retroactively using historical sales records. The higher the cost basis you can prove, the lower your gains will be. You can estimate where you don't have proof, but be aware that if you are selected for audit, the IRS will not allow you any cost basis that you can't prove.
