This is much better information. I still doubt very much that your ancestors are buried in Hamilton parish churchyard.
You make your entries "Motherwell Hamilton" and this is confusing.
Motherwell was a "police burgh" from 1861 onwards. A part of the village/town of Motherwell lay, until the boundary changes on 3rd May 1895, in the parish of Hamilton. This was that part of Hamilton parish north of the river Clyde up to what is known as Motherwell Cross. This would have included all of one side of Brandon Street, Part of Muir Street, Watsonville miners rows etc.
The postal address of anyone living in the burgh of Motherwell would not have included the word "Hamilton" (referring to the town or parish of that name). So, it's best to forget about Hamilton for the moment.
People who lived in the village (later the town) of Motherwell, unless they were Dissenters, all worshiped in the parish church of Dalziel. They were also buried in the parish churchyard(s) of Dalziel. After 1895 all of the burgh of Motherwell was within Dalziel parish. So, perhaps your grandfather was in a family plot in one of the old Dalziel burial grounds (there are 2 of them) but, having checked the Monumental Inscriptions lists, his name isn't there. Do you have any other family members names? His father & grandparents?
The parish council of Dalziel opened a new cemetery (now called the Globe Cemetery) but that didn't happen until 1876, so he can't be there! And, our other cemetery at Airbles didn't open until about 1905.
Now for the Brandon Hotel! I have to admit, that was a new one for me. I have checked through the old directories and did find some mention of it. My guess is that it was a bar with a couple of rooms above. It was around the Cross area somewhere but I can't pinpoint it exactly as yet.
It may have changed names over the years and it could be that it is now the "Horse Shoe Bar", a well-known public house (Lud will know it and I think Sancti has been thrown out of it a few times

)
The 1911 Directory has an advert for the Royal Hotel as "Motherwell's Only Hotel". This was what we knew as "Duffy's" and was in the middle of Brandon Street and was never known as the Brandon Hotel.
(It was the Royal Hotel as the Emperor & Empress of the French had spent the night there because the bridge between Motherwell & Hamilton was flooded. They were on their way to visit the Duke of Hamilton at his palace).
Here's what I found in the old directories -
In the 1875 "Motherwell Almanack" it lists Mrs D. Hamilton, Brandon Hotel, Cross.
(There is also a James Hamilton, baker, the Cross, any relation?)
In the 1894 and the 1899 - 1900 Motherwell directory it lists, under "Spirit -Dealers"
David Hamilton, 11 Muir Street. See the wonderful full-page advert in the 1894 book below.
(The 1894 book has James Hamilton, baker, 7 Brandon Street).
I still have one more book to check, if I find anything I'll get back to you. We are still no nearer to finding the burial places! If your grandfather was born here in Motherwell there must be a family burial plot around somewhere. His ancestors names may help.
For some reason I am not allowed to upload the pictures of the directories, something about having the same file names! I will post this and try to send them afterwards.