Comedian Brand, 48, was last week accused of rape, sexual assaults and emotional abuse during a seven-year period.
He denies all of the allegations, which are currently being investigated by the Met Police, the Los Angeles Police Department and his former exployees the BBC, Channel 4 and Banijay UK.
Brand states all of his relationships in the past have been consensual.
While Gallacher and Brand are on speaking terms, the victorious 1995 European Ryder Cup captain is said to have been "concerned of the age gap" in the past.
Laura is 12 years younger than Russell.
They share two children, Mabel and Peggy, and are currently expecting a third child.
According to a family friend who spoke to the Daily Mail, the couple first split in 2007 "at the behest of Bernard".
The publication reports the 10-time European Tour winner was "concerned about the age gap and begged her to end it."
A source told The Mail: "Bernard is a very strait-laced guy, with no side to him. So in that sense he and Brand are chalk and cheese."
Laura and Russell have reportedly broken up and got back together four different times throughout the years.
But Laura is said to be standing by her husband, whom she married in 2017.
Laura deleted her Instagram account amid the serious allegations against Brand.
Gallacher's other daughter Kirsty Gallacher, the former Sky Sports presenter, is said to also be standing by Brand.
Bernard Gallacher, 74, last week told Mirror Sport that LIV Golf's Brooks Koepka was "forced" to be picked in the United States Ryder Cup team.
He also considers the Americans will be a weaker team in Rome as a result of losing both Dustin Johnson and Bryson DeChambeau.
Gallacher, who represented Europe at the Ryder Cup eight times and three times as captain, revealed earlier in the year how more needs to be done to make golf a more inclusive, diverse and accessible sport.
Every UK golf club should offer scholarships to local youngsters, and ‘archaic’ dress codes should be binned, said Gallacher.