I think before you submit any apology you need to read the appropriate guidance that the school should be following which is Guidance on Controlling access to school premises, published 27 November 2018.
What it says is
"Schools can bar someone from the premises if they feel that their aggressive, abusive or insulting behaviour or language is a risk to staff or pupils. It’s enough for a member of staff or a pupil to feel threatened.
The school should tell an individual that they’ve been barred or they intend to bar them, in writing. Letters should usually be signed by the headteacher, though in some cases the local authority, academy trust or proprietor may wish to write instead. The individual must be allowed to present their side. A school can either:
*bar them temporarily, until the individual has had the opportunity to formally present their side
*tell them they intend to bar them and invite them to present their side by a set deadline
After the individual’s side has been heard, the school can decide whether to continue with barring them. The decision should be reviewed within a reasonable time, decided by the school. "
From your posts it does not seem as though the school have followed this procedure but just gone immediately to "your barred". I would reword the letter to ask that before any final decision is made that the school follow the procedure above and let your father put his side of the situation to the school. There is every opportunity if the school do carry out the correct procedure for your father to verbally express his apologies and regret for the incident whilst making the point that it was him being attacked that caused the incident.
The other part of the guidance is that it is not meant to be punitive long term and that if the school do consider that a ban on entering the school grounds is necessary that it should be short term, for instance till the Easter holidays. In the interim your father can take the three children to the school gate and then the three will have to make their own way into the classrooms. You could alternatively argue that once the children are on the school grounds that the school is "loco parentis" and therefore need to make arrangements for collecting the three kids at the school gate. That might just clarify the school's mind as to how to handle this situation.