She will be exempt, on up to $250,000 in capital gains. Even though she has been in a nursing home, the house is still her principal residence for the purposes of the home sale exclusion.
Reference: https://www.irs.gov/publications/p17/ch15.html; which says "Under this exception, you are considered to live in your home during any time within the 5-year period that you own the home and live in a facility (including a nursing home) licensed by a state or political subdivision to care for persons in your condition"
