Should I get divorce or separation

Good evening, I am trying to determine which option would be the best for myself & my children. I’ve been concerned for the last year that my husband was cheating & in recent months I have gotten the proof I needed. I have emails & phone records from the last year showing inappropriate contact between my husband & multiple women. I also walked into my bedroom one day only to be handed another woman’s earring that my toddler found on the floor, when I searched the rest of the room I found missing condoms & an empty pack of male enhancement pills. My husband & I have not been intimate for months. I suggested counseling, but he refused to go to more than one meeting. He has been going out multiple nights a week to local bars drinking away our money until 3-5 am in the morning. After months of trying to talk with him to find out what the problem was I finally began to get questioned from friends & family members about a strange car at my house while I am at work on the night shift. I have since discovered the strange car is my husband mistress, I confronted my husband & he refused to stop seeing this other woman.
My issues now are:

  1. Can I forbid him from living in the house if both our names are on the mortgage & the loan?
    We bought the house together after we were married, I’m not sure if I want to stay in the home with our children or if I want to sell it, but I no longer want my husband living in the house. I have come home from work on more than one occasion & found his mistress in our home with him while all of our children were home. For the last two months he has repeatedly told me that he would move out, but has yet to do so. He comes & goes from the home as he pleases eating the food I fix to take to work & for our children but does not replenish the groceries.

  2. Can I get a no contact order or restraining order against his mistress to prevent her from being in our house or around our children?
    After catching my husband & his mistress at my house I suddenly have nails in my tire the next night. I went to school with this particular woman & I know she was & still is a heavy drinker & I am concerned about her mental state. I also know that she has 3 children of her own that she does not attend to as she leaves work & spends all night drinking in a bar (with my husband) & I do not want a person of her “moral character” around my children.

  3. The mortgage is a VA loan through my husband’s military service, if we divorce will I be able to keep the VA loan or will I have to refinance?
    The mortgage currently had a very good rate & if I choose to stay in the home with our children I do not want to have to go through the process & financial cost of refinancing a home.

  4. Can I prevent him from having unsupervised visits with the children without a custody settlement?
    I have tried to give my husband full access to the girls as I work night shift & finding a babysitter is hard. Unfortunately my husband has been drinking more & more around the children & as I stated above is bringing his mistress to the house while I am at work. The drinking has gone beyond a social drink or two, when I come home from work in the morning I see a 6 pack or more & sometime liquor bottles empty in the trash.

  5. I make a substantial amount more than my husband, if gain full custody of the children will I still be able to hold him responsible for child support?

You cannot order him out of the home yourself, but may file for what is called a divorce from bed and board based on adultery and habitual drunkenness (judicially ordered separation) and ask the a judge order him to leave the home.
You cannot get a restraining order against his mistress.
You will need to re-finance the mortgage in order to complete Equitable Distribution and remove him from the loan. You may however either work out an agreement with your husband, (or if in court ask the judge) to allow you a year or so to refinance.
You both have equal rights to the children until you have a custody agreement.
If you have full custody of the children you will be owed child support.