Thank you! I'm leaning towards the dual core processor, too. And then 3 GB RAM (though perhaps I'll gift her one extra GB RAM). It'll be Windows 7 and from its performance on my slightly old Acer Aspire One I'm feeling confident the hardware will be a good choice for the purpose.
Thanks for the suggestion of using remote control. I've been thinking along the lines of it myself, I've just only had little experience using it. I'm probably going to have the PC sent to my home, and then set it up and then visit and bring it with me. It'll be the easiest, I think