Can my wife force me to move out of our marital home? I have always paid the mortgage as she doesn't work. The house is in just my name. She has left the home with our two sons and gone to live with her mother. She has also refused to let me see our children.

Not without a court order. Find yourself a good divorce attorney.

She can not force you to move out without a court order as Emland said. BUT she can possibly force you to sell the house and split the money or force you to pay her half the value of the house and make you move out with a court order.
Beat her to the punch and get a good divorce attorney as Emland said.

What reason do you need to apply for a court order?