I think that some people just don't like that close contact, and not being able to see the face makes it even more uncomfortable. I am sure that Eeyore was commisserating with "mom" for being left behind while the rest of the family was at the buffet table... nothing more. It would be entirely within Eeyore's personality to seek out the other alone soul in the room and try to make her feel better. The person in the costume was just staying true to the character by offering comfort... I think it was very sweet, and your mom took it the wrong way. She, having never been to a character breakfast probably was not expecting this, nor was she wanting it.
Certain cultures and certain age groups may be uncomfortable with characters showing affection (there are but so many ways for them to communicate, since they aren't face characters and cannot talk). They can read some people, but they aren't mindreaders... If you are one of these people who aren't touchy/feely, and don't like others to be, please do yourself and the characters a favor, and let the hostess/ server know, so they can pass it on to the characters. They are not out to make anyone feel uncomfortable, and would probably be very upset if they knew they had irritated anyone in anyway.