Firstly, if the restraining order states that your son must not contact the mother, or cause others to contact her on his behalf, then you contacting her will be a breach of the order. However, depending on the type of restraining order, the order may also state that there is an exception in respect of trying to arrange contact with the child. If you have a copy of the order, please attach it using the paperclip and I will review it for you.
Secondly, even though there has been violence and the child suffered an injury, it is not at the level where the courts would consider that no contact whatsoever needs to take place, and therefore it is likely that your son will be able to gain some contact - probably supervised for a period of time.
Your son is obliged by law to try mediation to see if that will resolve matters. You will see from the attached application form that the form must be signed by a mediator before he can apply to the court. Whilst your son will still need to attend a MIAM to get the form signed by the mediator, mediation clearly will not work in the circumstances due to the restraining order and previous conviction. Therefore, once the mediator has signed the form, your son can proceed to apply to the court.
The form you need is called a C100, which you can find here: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/734888/C100_eng_0818.pdf
The form needs to be a) signed by the mediator, b) filled in by your son (he is asking for a child arrangements order to spend time with his son) and then c) copied three times (with a fourth copy which he will keep for his own records). He must then take or send the original copy plus 3 copies to the family court closest to where the child lives.
You can find the right court here: https://www.gov.uk/find-court-tribunal
The fee for filing is £215, but your son may be entitled to fee remission, see here: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/634329/ex160-eng.pdf
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