I actually don't find Pat all that unbelievable either.
As others have said, she is just so relieved that her DD has found someone who appears to adore her and with whom she is happy, that she simply blanks out the bits of Rob that don't square with that.
That's the thing about abuse - abusers don't just groom their victims, they groom everyone around them. They put a huge amount of work into appearing a certain way (charming, loving, concerned for their victim's welfare etc.) for the benefit of their victim's relatives and friends. It's one of the tactics they have, to isolate the victim - the ones they can't charm (like Kirsty and Ian) they try and get rid of and the ones they can't rid of, they charm.
Pat and Tony are being groomed. Pat more successfully perhaps, but that's because we haven't heard much from Tony recently. Tom less successfully, so he's kept as much at arm's length as is possible within a family like that.
Anyone can be groomed by an abuser. Even a radical, Greenham-common visiting, feisty feminist like Pat.
Although I think they could have done it more carefully, more gradually, more thoroughly, to show how it happens. The fact that so many people disbelieve it, just shows that it hasn't been done as skillfully as the main relationship, between Hellin and Rob. They needed to write a few more scenes which they presumably didn't realise were necessary.