Spouses "kick each other out" all the time. Personally, however, unless there's a safety issue involved, I wouldn't recommend doing that. If she bought the house before the divorce, yes, it is at least theoretically her separate property, but her husband could make an argument that since any income she's paid the note with since marrying him is actually community property, there's been a mixing of "their" money into "her" house, giving him an interest in the house. Hopefully, that won't be an issue, but it might. I don't know what the situation is or how strained their relationship is right now, but ultimately, both parties are usually better off both emotionally and financially in the end if they can try to sit down, calmly talk things out, and come to an agreement. Highly contested divorces seldom really benefit either party, and "kicking him out" might be the first blow of a long, drawn-out fight that would end up hurting her, too. If she's really concerned about getting him out quickly, filing and immediately asking for temporary orders from the court might be the way to go.
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She can certainly ask to have him moved out. Understand that while the house is hers, mortgage payments made during the marriage are likely paid with income generated during the marriage, or community funds. Her husband could get half of those payments back, but not the home. However, if he used and benefited from the payments by living in the house, most courts are not going to make her pay it back as it is comparable to renting the space.
She should still hire a lawyer, if just to help push this divorce through. It sounds like it will be contested, and contested divorces can drag out a year or two easily without someone pushing them through the court system. On the other hand, if it is agreed, she could be done as quickly as 60 days from the date of filing.
This answer is intended for informational and educational purposes only and should not be considered legal advice nor forming the attorney client relationship. This attorney is licensed in Texas.
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