Should I put my Ex-Girlfriend on the title of my house?

I purchased a property under my name with at that time my girlfriend whom I share a child with. Right now we broke up and parting our own ways. She does not want to move out nor pay for this place until I put her on the title of the house even though I told her that in this case I will have to move out, rent another place and stop paying for the current house (putting it in foreclosure). I told her that I want to build equity in this house all of which will go into our son's savings/college account upon sale which I plan to do within 7 - 10 years. I love my son to death and in no way have any other thoughts other than giving him a great ($50,000+) present upon college time. She does not believe me and is telling me that the only way she would move out if I put her on the title of the house. On top of that I am willing to pay $1200/month cash as child support without involving any courts or lawyers to save her even more money. Would putting her on the title be a smart thing to do on my end? Other option which I do not want to excersice because I do not want to cause any harm or discofort to my child would be to evict her.