'You and her' drink? I agree with Crimson though... "You both drink" sounds MUCH more natural in English.
Wiktionary gives trinki for 'comsume liquid through the mouth' and drinki for 'consume alcoholic beverages' but I think that's an oversight by the contributors rather than an actual distinction and these are just alternative spellings. I imagine it probably has the same level of implication as English.  Actually, Lernu.net confirms that this is an actual distinction in Esperanto and not just a matter of spelling.
is 'vi', 'you' in Esperanto only singular. Because if it were able to represent 'more than one' it makes more sense to just say 'you're drinking' or 'you both drink'. That would erase the klunkiness of the phrase.
Or is this a completely regular and acceptable structure in Esperanto?
Esperanto is a bit like English in this matter. "You" and "vi" can be either singular or plural, but there is a poetic/archaic pronoun in both languages for the second person singular. In English, it is "thou", and in Esperanto, "ci". "Ci" is rare - La Plena Ilustrita Vortaro (PIV) says: " ci estas tre malofte uzata". ("Ci" is very seldom used")