I am sorry for what you and your children are experiencing.  The games that people play can be very cruel and ruinous - see my CZ blog, "Coping With Betrayal."

I don't know what country you reside in, and I believe that you wrote that the ex wife has signed divorce papers in October.  Does this mean that you are legally divorced, then?  Or, were those papers a legal separation?  WHY are you still living in the same place?  Do you have an attorney representing you in this, or have you had legal representation?  If so, what does your attorney say?  Have you filed for legal custody of your children?  Is there a custody/visitation order by the Court? 

A competent divorce attorney will cost money, but will be worth every cent.  In the United States, what your ex-wife is doing is cause for legal action and is called, "Alienation Of Affection."  This is when a parent tries to turn mutual children against the other parent before, during, or after a separation/divorce matter.  You have ample proof of her manipulations, and this information would be priceless in the hands of a good divorce attorney.

If the woman has signed legal papers for separation, there ARE means to force her out of the mutual  home.  However, this might cause financial difficulties for you both.  Either way, it is worth it to get someone who is that messed up out of your house, and out of your life. 

Having typed that, it is important to learn how to separate your emotions from the tasks at hand.  Divorce is always ugly, particularly when children are involved.  NOBODY wins except the attorneys who are not emotionally involved and will always get paid, regardless of the legal outcomes.  So.........learning how to process your rage, hurt, anger, etc., will be very, very important in the future.  Leave your children out of all adult matters - do not discuss these matters in front of them, or with them.  Of course, a 3-year-old isn't going to be able to understand or ask about what's going on, but it is vital to keep the children out of these matters. 

I strongly suggest that you speak with your divorce attorney, immediately, to learn what steps you can take to get her out of the house, to file for sole custody of your children, and to make sure that your children are safe.  There is nothing "good" about bringing a man into young children's lives under such circumstances, and they will be the oines to suffer.

I would also strongly suggest that you contemplate some counseling therapy, just for a little while, to help you process these dreadful betrayals, and sort out coping skills that will benefit you and your children in the long term.

Brightest blessings of courage to you.