The rules for excluding the gain from the sale of your main home requires the the home be owned and occupied as your main home for 2 of the last 5 years from the date of the sale.
If those requirements are met, then your mother, filing as Single, will be able to exclude up to $250,000 of gain. Since you are filing as Married Filing Joint, you would only be able to exclude up to $500,000 of gain only if your spouse was also an owner of the property and met the requirements for excluding the gain. Based on your statement that the house was owned by your parents and you, you would only be eligible to exclude up to $250,000, but not up to $500,000.
As for reporting the sale, it will depend on the percent of ownership for each party. If your father's share of the house was split between you and your mother, then you would each report half of the sale proceeds and half of the cost basis. If there was a different split in the ownership after your father's death, then only report each person's share of the ownership on their own return.
To learn more, see the following TurboTax article: Is the money I made from a home sale taxable?
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