Hi Jeff, I was at the Archives again and had a look through their records but unfortunately turned up nothing for Robert Roberts.
I looked at the 1896 copy of the local paper the Llandudno Advertiser but could see no obituary notice or anything about the family tragedy
I then looked at the 1939 register for England and Wales and could see no person with the matching date of birth of Robert, the nearest match was the one that you had already found at Ty Newydd Barrog.
I rechecked the burial records for St Tudno's Church but there was no record for Robert there. Those records are for the Church Cemetery only though. There is a much larger cemetery there but it is Council owned and those records are I believe held at the Crematorium in Mochdre
I know for a fact from Billion dollar graves that there are a number of Robert Roberts buried there in the new Cemetery at St Tudno's but don't know if the details match your Robert.
One I was looking at on Billion Dollar graves was a Robert William Roberts who died in 1975 but his wife Winifred Catherine died much earlier in 1932. Unfortunately his age was not put on the headstone so I don't know any more details other than that.
When I looked at records from Find My Past there was a Robert Roberts born 1892 who died in 1961 and the death was registered in the Conwy District at vol 8a pg 167 death quarter 1
The records also showed marriages of a Robert W Roberts in the Conwy District in 1915,1917, 1922, 1923 and 1924 but again there is no evidence to say that anyone of them was your relative.
However local papers like the Llandudno Advertiser and North Wales Weekly News reort marriages and obituaries and may be able to confirm things one way or another
Before I start to look in the papers I would appreciate it if you could tell me what you know for certain about Robert, wife children etc just so that I have something positive to work with