Yes, it's contact, but I can understand where your Mom was coming from. An e-card feels much less personal - you can't display it the way you can a real card, you don't get the interaction and personal contact you do with a phone call or visit, so you end up with the worst of both worlds, as it were. Also, they can come across as very generic and impersonal.
It sounds as though you were able to make the point that you had made the card with her in mind.
It sounds as though your Mom was a bit rude in how she let you know she was disappointed, but I can understand why she felt that way, and now that you know, I think it would be nice if you were to get a physical card and mail it, or to phone her, for future events. (even if this means designing it, or helping your daughter to design it, on the computer, and then printing it off for her to send!)
I think if you plan to send something only electronically, a personal e-mail is often better than an e-mail, as it is more obviously personal.