Because where my wifi is situated you can't pick up a signal anywhere else in the house and also my mums modem isn't a wireless one so she will need a cable when in her room and when downstairs.If you don't mind me asking, how come you require an ethernet port?
I was also going to suggest a tablet, netbooks are another alternative which could fit your requirement as it'll come with one and Wi-Fi. They are a little underpowered by as you say if it's only for browsing / emails and videos should be fine.
Some kind of AMD fusion or Intel Atom set up. What kind of OS are you looking at? My mother wouldn't have a clue with 8 lol.