Hi Lynne,
I think there has been a bit of confusion as to where Tywyn/Towyn Llanrhos is. 150 years ago the postal directory refer to the hamlet of Tywyn in the parish of Eglwys Rhos which is centred around Pentywyn Hill area. Today it's called Deganwy and is over the river from Conwy town. There were several houses known as Ty Newydd one of them still remains today called Lavender Cottage. There were a group of houses also called Ty Newydd in the area were Garth Motors stands today and there is a reference to a John Roberts farmer living there.
There is a very informative site with some lovely photographs of various houses and churches in the area, lists of houses and occupants and a map from 1864 that will give you an idea of where all the boundaries for these hamlets are. Sorry I can't post a clickable link as I haven't worked out how to do that yet. Google 'Tywyn in Victorian Times Researched by Fiona Richards.'It will give you an idea of the area they lived in. I live nearby and very often pass that area and also had family living there on the 1881/91 & 1901/11 Census so if I can help further please ask,
Kind Regards,
Ellen