There are two-way prepositions that can be either accusative or dative. If the preposition in the sentence answers the question "where to?" (meaning the object in question is at work at reaching its destination) it is accusative. If the sentence answers the question "where?" (meaning the object in question is already at that place) it is dative. In this case, the "best wishes" are directed "to" your mother, so as it implies motion, it's accusative.
You're kinda right though, 'to' would only be used for movement, and 'on' only for location. So it's fair to say that when 'an' translates to 'to', it takes accusative, and for 'on' it takes dative. (Although if it translates as 'onto', it's movement, so it's accusative). This is only for two-way prepositions though, 'zu' can mean 'to' as well, but it isn't two-way, and it always takes the dative.