If you are married you have only two filing statuses: married jointly or married filing separately.
However one of you can claim head of household only under the following conditions.
1. She is considered unmarried at the end of the year.
2. She paid half the cost of keeping up a home for the year.
3. Your child lived with her more than half the year.
4. Your spouse did not live with you for the past six months at the end of the year.
However, this may raise a flag with the IRS. Just know that, the IRS considers the absent spouse to be part of the household if that parent is temporarily away for things like: work, school, vacation, sickness,etc.
This will involve the issue of where you tax home is rather than where your primary residence.
Generally, the primary residence is where you return home to where your children and wife are; and there for the IRS will not likely allow this on audit.
BotXXXXX XXXXXne, if you are returning for regular visits to visit your wife and children, the IRS is going to treat the home maintained by your spouse as your primary home.