Mileage Plus Dining = iDine, and it is not possible to register the same card with more than one iDine program.
If this is a response to my post;
While I don't disagree with what you're saying.. I don't 'register' my HA visa with their Xtramiles program. Shop/dine with thier card at an Xtramiles merchant, get Xtramiles, in addition to those from UA's idine. That's like saying I won't get bonus miles for booking UA with Chase UA Visa because the card is registered to idine. Unless you've specifically tried with the HA Visa and had bonus miles from one or the other denied, I'll take your post with a grain of salt.
If it's not a response to my post; disregard above.