If the house is in your name solely and neither your wife nor the adult child pay rent then in principle, absent a court order to the contrary or some other contractual claim to an right to occupy the premises, they are simply your guests and you can terminate their welcome without notice and essentially, just change the locks, although you would have to give them reasonable opportunity to leave.
However, if your wife is a co owner on the title of the property she is entitled to reside at the property the same as you until such time as a court order is made and if neither of you can agree for the other to move out you will have to wait until a court makes orders about the division of the property and or living arrangements.
Despite the above, even if the property is solely in your name, either of you can apply to the family court for interim orders regarding occupation of the house and if your asset position is such that any property division will entitle her to a share of your property, it is possible a court could make orders allowing her to stay in your property, and furthermore if you eject her and/or her son in a way which appears unreasonable and particularly if it creates unnecessary expense, the court could form a dim view of your approach and it may count against you in any ultimate court proceedings to divide up your assets.
My suggestion is that you simply write to your wife pointing out that impracticality of you both living in your home, and requiring her to move out within a week or so.
In the long run I think it is in your interest to behave in a way that is reasonable as it will reflect more favourably on you if the matter ultimately ends up before the court.
I trust the above assists.
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