These are the definitions under the General Statute 50-20:
"(1) “Marital property” means all real and personal property acquired by either spouse or both spouses during the course of the marriage and before the date of the separation of the parties, and presently owned, except property determined to be separate property or divisible property in accordance with subdivision (2) or (4) of this subsection. Marital property includes all vested and nonvested pension, retirement, and other deferred compensation rights, and vested and nonvested military pensions eligible under the federal Uniformed Services Former Spouses’ Protection Act. It is presumed that all property acquired after the date of marriage and before the date of separation is marital property except property which is separate property under subdivision (2) of this subsection. This presumption may be rebutted by the greater weight of the evidence.
(2) "Separate property" means all real and personal property acquired by a spouse before marriage or acquired by a spouse by bequest, devise, descent, or gift during the course of the marriage. However, property acquired by gift from the other spouse during the course of the marriage shall be considered separate property only if such an intention is stated in the conveyance. Property acquired in exchange for separate property shall remain separate property regardless of whether the title is in the name of the husband or wife or both and shall not be considered to be marital property unless a contrary intention is expressly stated in the conveyance. The increase in value of separate property and the income derived from separate property shall be considered separate property. All professional licenses and business licenses which would terminate on transfer shall be considered separate property."
In reading this, the house is yours providing that you never had her name added to the deed. I am not sure how you would go about removing her from your home. Filing for divorce from bed and board, you would have to: "establish at least one of the six fault grounds enumerated in the statute: abandonment, malicious turning out of doors, cruel or barbarous treatment, indignities, excessive use of alcohol or drugs rendering the condition of the other spouse intolerable, or adultery."
I would suggest consulting with an attorney, get a separation agreement drawn up giving some sort of time frame that she must be out of the home…if that’s possible. Work out custody, child support, and equitable distribution leaving the home off the distribution list.
There are other issues besides who the house belongs to. If there are children in the picture, this may be a little more difficult. If you are going to force her out of the home, custody will need to be worked out prior, unless you have already agreed on joint custody with equal time.(Best scenario for the children) Especially, if your STBX has no where to live if she leaves.
Hopefully, an attorney will answer because I’m not really sure what your best course of action would be other than to consult an attorney about getting a separation agreement drawn up and working with her to sign it.