Actually, it's not a matter of getting it "right" -- it's simply a matter of terms having different, more broad meanings back then. Both terms are correct based on 1600s usage; "cousin," "niece," and "nephew" were all correct, but the latter two were just more specific. It's kind of like identifying someone as your sibling or your sister -- both are correct, but one's more specific.
I'm very familiar with Jacob Remy, as he's the ancestor of a cousin of mine, through a line we don't share. I've helped her with her research, though, as until a few months ago, I lived in Virginia not too far from Westmoreland Co. for 22 years. I have Jacob Remy's wife Mary's maiden name as possibly Marmaduke, but I hadn't had a chance to do much research to follow up on that possible link.
I also agree that Patrick and Dorcas' daughter Mary probably died young before she married or had issue. Dorcas (--) Spence Jordan did a good job of naming all of her children and grandchildren in her will, so I'd expect to see Mary or her children listed in the will if Mary lived to have children.