You need to coall the local police or sheriff department and ask them to serve the restraining order for you. They can/will do so for free. They will knock on the door, and the woman to be served will answer the door because it is the police at her door. If she does not take the papers from the officer, they can simply leave it on her doorstep and file an affidavit of service stating that they left it with her because she refused to personally hand accept the papers. This should be sufficient for the court.
You can have the police serve her, and if they do and are able to produce proof of service for the court, then the court will issue the restraining order next week even if the other woman refuses to personally appear.
Attorney
8+years of experience in all matters of civil litigation and Hearing Officer/Arbitrator