This is where I get lost. I know all of my John Richard Edwards' (DOB: 13 Nov 1874) children and they do not match yours at all. I have a couple of references noting that his father was "Richard Edwards" and that his mother was "Caroline Tudor" so likely true. Just can't nail the specifics just yet. That's Caroline not Catherine.
It seems there was another Richard Edwards and perhaps a Catherine Tudor marriage in the same area of Wales with DOBs about the same. Your "Richard Edwards" perhaps is not my Richard Edwards. Or perhaps just a different marriage, an entirely possible scenario.
My John Richard Edwards came to the USA in 1887 and is buried in Manchester, NH. Had children named: John Richard Jr., William Daniel, Christina E., Dorothy Campbell, Elizabeth Euphemia, Isabelle Shakespeare, Luena M, Caroline Ellen, Clarence Robert.
If you or anyone else wants to take this back and forth offline, send a message directly to my thedwards1 Ancestry.com User ID and we can explore more, perhaps with shared email addresses. The more we understand about the "maybe two" Richards the better chance we have of zeroing in on whose who.
Or continue something here as you wish.