If dad still has PR, despite the lack of contact, it is an application that needs to be made to court I'm afraid. It's a specific issue order application. You have a strong case on the history, but it is still something you need the court's approval for.
The application would be made on the c100 form, which is available in the www.gov.uk website.
An application costs £215 to make.
You will be exempt from mediation obviously, due to the criminal conviction and restraining order.
You could consider asking the court to list a without notice hearing (see section 6 of the form), meaning that you get to appear before a judge on your own to make the application with the father being notified after the event if you get the order in his absence. The court *may* consider this, in the circumstances.
Do remember that I can only give you my opinion.
Another lawyer may have a different opinion. If there was a black-and-white answer to every legal problem there would be no need for anything to ever proceed to court!
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