There are a few issues here.
1) A bible thumping, homophobic woman has had an affair. OK, this is hypocrisy. We can indulge in her discomfort.
2)
She is 40 years older, old enough to be his grandmother. That's just disgusting!!
Some people seem to be disgusted that a 19 year old male would find a 59 year old female attractive. Yet they criticize her for being disgusted that a 19 year old male, would find another 19 year old male attractive.
Is gerontophobia(?) that much different from homophobia?
I am neither a homophobe nor a gerontophobe (too old myself to be one, I suppose)
3) She used her power to get money for her lover and for herself. This is an abuse of her position and so she should resign.
4) But why should Peter Robinson resign? I don't like him. I don't like his views. It's not his fault that his wife was unfaithful and on the fiddle.
I genuinely feel for him. He has given great service and has been an honest politican as far as I know. There is no evidence that he has been dishonest. If there is, he should go.
I imagine the shock when he discovered that his wife had been abusing her position. In situations like this, people panic. He arranged for the money to be repaid. He should have insisted that she report it to the authorities, but I can understand why he didn't. I wouldn't fire him for it. It's very difficult to report your wife to the authorities. I am not sure that many people would do that.