Your mother may well qualify for the capital gain exclusion on her portion of the capital gain.
IRS Publication 523 states that if she became physically or mentally unable to care for herself, and she used the residence as her principal residence for 12 months in the 5 years preceding the sale or exchange, any time she spent living in a care facility (such as a nursing home) counts toward her 2-year residence requirement for the capital gain exclusion, so long as the facility has a license from a state or other political entity to care for people with her condition.
https://www.irs.gov/publications/p523#en_US_2019_publink10008997
You and your brother must pay capital gain tax on your portions of the capital gain. When you calculate the capital gain, be aware that the residence does not qualify for any step-up in its cost basis, since it was sold prior to the life tenant's death. As @rjs stated previously, gifting all or part of your portions of the gain will have no effect on your capital gain tax obligation.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
