You believe this is our Robert----(-Robert appears on the 1911 Census as living at Oakamore Colwyn Bay) I have the 1911 census for Mary Fox only husband and children living there . As I only have 1901 census for Robert's grandparents as the 4 off them died before next census .On the 1901 both sets of grandparents only live two doors apart and no Robert there.
I don't quite understand your comment regarding -
"Robert appears on the 1911 Census as living at Oakamore Colwyn Bay" as Rhuddlan's link to the home said that due to financial reasons the home closed in 1906 so there should be no Census for 1911 at Oakamoor Home Colwyn Bay.
If you have a copy of that 1911 Census would you please post it on here so I can see it.
If the Colwyn Bay home was closed in 1906 there is a possibility that Ethel and Robert were moved to another home and possibly in England but I'm only guessing until I see the Census record that I've highlighted above
It will be a week or more before I can get back to the Archives to have a look for anything
That address Penyfrdd is probably Penyffridd and there is a terrace of houses on the Great Orme Llandudno bearing that name, in fact I posted a photo of both Penyffridd and Wyddfyd Terrace on here recently. The information came off the school records and Ethel was at Penyffridd and Robert at Wyddfyd