It seems the police will only enforce a court ordered document.
That is correct. What you have at the current time is only a contract agreement that can be only be enforced under the common law of contracts. That means that you are entitled to change the locks on the home and to bar her access since there is a contract giving you sole possession of the home. However, if she enters the home, the police will not get involved.
Can I go to court and get some type of court order enforcing the agreement if she does come into the house without my permission.
You want to go to court and have the agreement incorporated and merged into a court ordered separation. Your attorney can handle filing for a hearing. In the meantime, if she enters, you would be able to sue her for the amount of any damages. Once the order is issued, then she would be in contempt of court if she enters the residence.
However, if she shows up at the house and starts trying to force her way in by physical violence, you can call the police and file charges for criminal domestic violence
. The magistrate will then issue a no contact restraining order
. However, that is not a good option.