The singular verb has should definitely be used in the sentence as you have written it. I would not however use 'them' to refer to the father too, since you know that the father is a 'him'. There are, though, things that are slightly incorrect in the sentence. Personally I would say:
A person who has perfectly good relations with their father, who loves their father, and has a great respect for him, could never shout at him like that.
But please note that, in your sentence, the verb 'has' is not actually being used with the pronoun 'they'as the subject. In the first instance your subject is a person who which clearly takes has as its verb. If however you were to use they as a singular subject, meaning 'he' or 'she', then you would use the plural verb, such as in:
As regards the person I have just mentioned, and as I understand it, they are going to be charged with obstructing the course of justice.
You would never correctly say they is going to be charged.