Open you the door isn't the exception at all. Most verbs capable of having both a direct and an indirect object don't readily accept the possibility of just specifying both objects without using any prepositions (but if/when you can do that, you always have to put the "indirect object" first).
There's a significant US/UK divide here, as illustrated by these Google Books results...
American usage: cash a check for me" (954), cash me a check (82).
British usage: cash a cheque for me (242), cash me a cheque (305).
As a Brit, I don't have any real problem with OP's exact usage and context, though I'm aware some people would find it anywhere between "slightly odd" and "totally ungrammatical". Taking it a bit further though, probably almost everyone would say that...
"Look who's in the driveway, Johnny! Go and open Auntie Ethel the door!"
...is "totally unacceptable".
EDIT: I don't really disagree with John Lawler's observation that the "ditransitive, prepositionless" dative alternation construction largely turns on whether the beneficiary ends up possessing the direct object. But it's not a hard-and-fast rule - particularly, I feel, in BrE.
As this source says, the above intended reception constraint [beneficiary ends up possessing object] comes with a certain amount of inherent fuzziness. And to illustrate that fuzziness, it gives actual "acceptability" figures for a few "marginal" constructions...
a: Could you iron me these shirts? [76%]
b: Could you wash me the dishes? [54%]
c: Could you clean me the windows? [47%]
d. Could you open me the door? [25%]
My own feeling is that this form is becoming more common (those figures were collected almost 40 years ago), and that it's more likely when the beneficiary is a pronoun (particularly, me). I'd be prepared to bet that if the above survey were repeated today, b above would score higher than 54%, but "Could you wash Mum the dishes?" would score significantly less.