Mark William Barron was a great-grandson of William1 Barron (and his 1st wife), grandson of William2 (and his 2nd wife Cynthia), and son of Jonathan Boyce Barron (and Maria Hogan). I see that you and I "talked" about these people last August (see above, in this same thread) & I referred you to Mark's Bible record which you can get from the DAR Library in Washington, DC. Did you get a chance to do that?
I don't know anything about Mark's children because I don't generally research children of non-direct children. (My husband is a descendant of Jonathan Boyce Barron's half-brother Nathan Barron.) Probably that Bible record would be helpful to you.
As to whether this line (the Surry/Keene group) goes back to the Watertown family - this is the line I was talking about in the last few days with you. I'm not saying they don't, I'm just saying that more competent genealogists than I have researched that family and show no link to Surry/Keene Barrons that you and I are talking about, nor do they have any information as to the origin of that family prior to immigration. I'm not sure anyone has proved or even claimed that the Watertown Barrons were from Ireland at all. And, of course, there is also no proof that "our" Barrons were Irish either, that I have seen, other than family lore -- that is why I was asking you what records you had found that got them back to the 1400s in Ireland.
As to our William1 being from Ireland, my guess is that story came from his descendants and so might be true. Also, William2 Barron's 1st wife was Jennet McCurdy, who was an immigrant from Co Antrim, Ireland. People in those days tended to marry people like themselves, so that could be a point in favor of Ireland. I would take the descendants' stories with a grain of salt, however. One of William1's grandsons lived to be quite old and had stories written about him in newspapers as he got old; many stories about him said that his grandfather (William1) was an officer in the Revolutionary War, which is most certainly not correct, so we can't always believe everything even family says. (Both William1 and William2 served, but neither was an officer; there was a New Hampshire Capt. William Barron, but he was an entirely different man from a different town.)