Ann,
You ask about the cause of death on Bernard’s death certificate. As I read it, it says: “Chronic bronchitis. 2 years (?) uncertified. No medical attendant.” Normally that box should record: a) the cause, b) duration & c) whether a doctor was present. So in this case you have cause, duration (I can't really make out precisely what it says though the word year seems to be in there) and that no doctor attended.
It didn’t become routine or mandatory to have a doctor attend a death until the 1890s when Parliament made it a formal requirement. The medical profession had till then put forward various objections. Arguments were along the lines of what was the point of them riding 20 miles over rough moors to attend a dead body? What good could they do then, when they might be spending that time more usefully with their living patients? The nub of the matter appears to have been money. If the patient was dead, who would pay them? Once the state said it would pay, their objections magically disappeared overnight, and they apparently happily certified every dead body in sight no matter how far away. Medical ethics can be quite baffling at times.
Bernard’s death certificate says he lived in Ballyvally. There’s only one Bernard in Griffiths in that townland and so I’d be surprised if plot 7 was not his home.
You ask whether Elizabeth would leave Ireland before her eldest son. That’s a question that might take an army of experts to answer fully. Ireland has some magnificent plays by writers like Brian Friel and Martin McDonagh. They often deal with “Irish angst”. The underlying themes often tend to be poverty, emigration, family jealousies and downright bloody-mindedness. A good example is “Philadelphia here I come” (Brian Friel). An uncle in Philadelphia offers Gareth O’Donnell in Ireland the opportunity to go to Philadelphia to work. Gareth is delighted but there’s the issue of his widowed father, his former girlfriend (who still loves him but reluctantly married another because "Gar" was too slow in courting her). And so on. Gareth has his ticket, a date for departure, and attends his American Wake (a farewell do) where his friends don’t really seem to care whether he goes or stays. All baffling for him. What about his lost girlfriend? Does he go or stay? Watch and see. It’s a magnificent play and should give you a good general sense of Irish emotions and relationships about emigration in the 1800s.
That said, I don't think there were any definite rules for whether a widowed mother would have stayed or gone. I doubt she’d have left her children with no-one to look after them but if they were adults, it’d be a different matter. Did they all get on? You don't have to dig very far in PRONI's wills to find some where a husband has specified the domestic arrangements after his death. Along the lines of “If my wife and my eldest son/daughter cannot agree to get on, the door from the kitchen to the front room is to be blocked up and a new door created from outside the building.” (Dividing the house in half, in effect.). Not every family lived harmoniously, so some might have wanted to go to the US when others might have wanted to stay.
You ask the best time to visit Ireland. I’d say in the afternoon because we generally don’t get up very early. Nobody here does much in the morning in my experience. Mornings would probably be no good to you. Try afternoons or evenings, that’d be my advice.
More seriously, any time of the year is suitable for a visit. Ireland is on the same latitude as Labrador and Alaska, so we get very long summer evenings and short winter evenings. If you want long evenings, come in May – July. But there are tourists here all the year round. If you like rain we can provide that nearly all the time too. (There’s a good reason why Ireland is so green). Pre-Covid it could get very busy in July & August so you need to book ahead then. If you want flexibility, come outside those top months and you’ll be able to book as you go if that’s what you want. Cheaper and quieter here off season.
If you want suggestions for tourist things to see and do in Co Down and Ulster generally, I have a list and can let you have it.