I thought this was an interesting technique (I can't remember how I came across it, maybe it was even one of the members here that posted it first). I've seen these types of videos pop up quite a lot recently (where you first mark and reward the undesired behaviour and then slowly transition to the desired - counterintuitive, but actually quite effective!).
In parallel, I might do short training sessions to slowly teach her to go to her "family dinner spot" (I would pick it strategically, so that she would be close enough so that I could reinforce good behaviour without getting up too much, but out of the way enough not to be a pestilence). I would work on longer durations of stay, and finally teach her that when I (or the family members) sit at the table, her job is to go to her designated spot and relax there. I find that when they have a clear expectation of what they are supposed to be doing, it helps many dogs chill out. But sometimes management is also all you really need.
I would probably just manage this during dinner and TV time, at least in the beginning, to break the already established habit of barking. I would put her on her bed or in her crate, whichever she is used to, and give her a long lasting chew, a kong, lickimat or something else to keep her occupied with her own chewing or licking project.
In parallel, I might do short training sessions to slowly teach her to go to her "family dinner spot" (I would pick it strategically, so that she would be close enough so that I could reinforce good behaviour without getting up too much, but out of the way enough not to be a pestilence). I would work on longer durations of stay, and finally teach her that when I (or the family members) sit at the table, her job is to go to her designated spot and relax there. I find that when they have a clear expectation of what they are supposed to be doing, it helps many dogs chill out. But sometimes management is also all you really need.