If you are not married, and it is soley your house, you would need to file an eviction against her in the local municipal court. This would allow you to obtain a court order to evict her and then change the locks to prevent her from coming back to live. You have no obligation to find her a new place to live, with or without the children.
However, if the children are yours, and she leaves with the kids, figure you are going to be paying child support through the CSEA if any turn out to be yours.
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