The motorcycle enthusiast - who is accused of cheating on the actress with at least four other women - has reportedly told his spouse that the problems in their marriage won't come between her and his three kids, in particular his six-year-old daughter Sunny who she is especially close to.
A source said: "Jesse told Sandra he's going to make sure she sees Sunny as often as she'd like when he has her. She's spoken to her and the other kids and has said she's not going to lose them."
Despite his reassurances, Jesse is said to have found it difficult to explain to Sunny - whose mother is his second wife Janine Lindemulder - why Sandra isn't spending time with her at the moment.
The source added to America's OK! magazine: "He told Sunny that he made some mistakes that really hurt Sandra's feelings and made it impossible to trust him right now, so she went away to try to not be so angry."
Despite her closeness to Jesse's children, including his son and daughter with first wife Karla, sources have insisted that 45-year-old Sandra - who is in telephone contact with Sunny every day - has no plans to bid for legal custody of the children if she and the 'Monster Garage' host divorce.
Her representative said: "There have never been any plans for Sandra to adopt any of Jesse's children."
Jesse - who is also accused of sleeping with stripper Melissa Smith, photographer Brigitte Daguerre and an unnamed mistress who is represented by high-powered lawyer Gloria Allred - has spoken about his regret over the upset and hurt he has caused Sandra.
The 40-year-old TV personality said: "There is only one person to blame for this whole situation, and that is me. It's because of my poor judgement that I deserve everything bad that is coming my way."
Despite Jesse's regrets, it has been claimed that Sandra is planning to file for divorce.
A source said: "She's had enough. She's ending the marriage."
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