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Dear JACUSTOMER - Unless there is violence the matter is between the two of you. The court is not going to get involved in private family matters. Both you and your wife have an equal right to the premises so each of you can invite who you like. Obviously something like this can put a heavy strain on a marriage but there is really no legal solution to the problem. This is no different than any other martial decision concerning the family home so you and your wife need to work this out between you as the courts are not the proper place to solve this kind of dispute.
You may want to try to talk to a family counselor for some advice on how to handle this problem as I would hate to see your marriage break up over this. I'm not certain how long your mother is staying but you may want to try to keep the time a minimum or possibly have her stay in a nearby hotel. Those are not legal solutions but just suggestions. Legally you have a right to have anyone you please in your home as does your wife.
Visitation and support are separate issues and in order to deal with each she would have to file some type of court action such as divorce or legal separation. I cannot imagine any court denying you visitation just because you moved out since that has nothing to do with the children. As far as paying the mortgage etc. it is possible he could get a court to award her some temporary support, both spousal and child support while any court action is pending. Of course if she simply tries to deny you visitation without going to court then it may be you who has to go to court in order to see your children.
There is no basis to deny child visitation under these circumstances.