Hi Connemmara,
I think you've already identified the chief cause of the behaviour problem yourself
---- she would give him titbits more than myself so they are "friends" ----
I think it would pay to ask your sister to tell you why she does this.
If, as you hinted, she really is afraid of the dog (dogs in general, even) then maybe she feels that tidbits will placate it in some way?
All this has achieved, to date, is cause the dog to do as you described. It has learned that barking will result in it being allowed indoors where it can make a beeline straight to her position at the dining table - instead of at its master's side!! It knows her position is where 'people food' is dished out - much nicer than that dogmeat stuff that you usually give him.
It would be silly of me to suggest devious motives but you did say she sometimes has a go at you for having poor control over the animal. If she secretly wanted you to get rid of the dog then causing it to become disruptive at family gatherings (wittingly or unwittingly) is certainly one way of achieving that goal. Obviously, it would be unhelpful to actually challenge her on that point...
If you could gradually persuade her that it is her habit of dishing out these 'special treats' which is causing all the disruption in the first place and, at some stage, make it clear that this should cease from now on, then at least you're making progress.
Of course, as long as you continue allowing it indoors because it is barking, then it will continue the barking habit, regardless of the fact that the treats have stopped.
Furthermore, since the unwanted behaviour only occurs once per week the corrective treatment can only be applied once per week and it could take many weeks to change the dog's behaviour, which means sitting through several disrupted Sunday lunches.