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The exclusion only applies if you owned the home and lived in it as your main home for at least 2 years before the sale.  For example, if your mother lived in the home but you did not, then your mother can use the exclusion ($250K since she is single) but you can't use the exclusion.  Your gain will be fully taxable.

To determine ownership percentages and the amount of gain, you will need to review the deed, and how the home was transferred into your name.  This can be very complicated, and if your parents "gave" you share of the home, thinking they were saving you from probate, they may have also given you a big tax bill.

You probably should get this reviewed by a local tax professional.  However, I can attempt to guide you a bit and let you know some of the issues.

1. If you were given a share of the house by deed transfer or quitclaim deed, but the deed says your parents have "right of survivorship" then you are not really the owner and owe no tax.  Your mother would report all the gains, and qualify for the exclusion.  Right of Survivorship means you have no rights in the home unless both your parents had died, so the IRS views you are not responsible for any of the taxes.  If your mother gives you a share of the proceeds, that is a gift from her to you, and she must report the entire sale on her tax return.

Your mother's gain is the difference between her adjusted cost basis and the selling price.  Her adjusted basis is computed as follows:

• For half the house, her basis is half the cost she originally paid, plus half the cost of any permanent improvements she made over the years.
• For the other half of the house that she inherited from her spouse when he died, her adjusted basis is half the value of the home on the day he died (called a "stepped up" basis).

So let's say the home was purchased in 1980 for $50,000, and in 2000 they renovated for another $50,000.  When her spouse died in 2015, the home was worth $310,000.  Your mother's basis is $50,000 (half of $100,000 costs) plus $155,000 (half the fair market value when her spouse died) for a total of $205,000.   If the home sells for $400,000, her gain is $195,000.  If she has lived in the home for 2 of the past 5 years, her gain is not taxable since it below the exclusion limit.

Additionally, if she moved out recently because she had to move into assisted living or a nursing home, but she retained ownership, that counts as if she still lived there, to qualify for the exclusion. 

2.  Suppose you were gifted a share in the home "in fee simple".  Then you are an equal co-owner with the other owners and have the same rights and tax responsibilities.  The IRS will assume you own equal shares (1/3 each) unless the deed says otherwise.  Then when your father died, you inherited 1/6 of the home from him (half of his 1/3 share, get it?), making your total share 1/2.  Your mother inherited the other 1/6, making her total share also 1/2. 

Now when selling, basis gets tricky to compute.  Again, let's say the home was purchased in 1980 for $50,000, and in 2000 they renovated for another $50,000.  When you were gifted the home in 2010, you were also gifted your parent's cost basis.  Since the total cost basis at this time was $100,000, then each of your cost bases (mom, dad, child) is now $33,333.  When her spouse died in 2015, the home was worth $310,000, and the fair market value of your father's share is 1/3 of that or $103,333.  Half of that gets added to your basis, and half to your mom's basis, so your adjusted cost basis becomes $85,000.  If you sell for $400,000, then each of you reports a gain of $200,000 minus $85,000 equals $115,000.  If your mother lived in the home, she can exclude the gain.  If you did not live in the home, you can't exclude your gain and it is fully taxable.

As you can see, this requires a lot of documentation.  If audited, the IRS does not award anything you can't prove, so you will need to locate any records that bear on the cost basis.  The original purchase of the home, cost of improvements, fair market value when your father died.  (The cost will be in the county records, and the value on the date of your father's death can be obtained from a real estate appraiser.). You need to know exactly how the deed was written making you a co-owner (there are other variations besides the 2 main ones I mentioned).  A local tax professional will know what questions to ask and what to look for, and will be able to interpret the deed or will know an attorney who can check the deed for you to determine how the sale will be treated.