I'd generally strongly in favour of bills bearing some approximate relatoin to costs but in this instance I'd have let it go, reasons being:
(1) of the six diners, four were part of your direct family, the other two part of your extended family;
(2) the differences you're talking about [12 'extra' drinks ordered, you paying for one third of the extra spend, i.e. in effect for 4 drinks that were nothing to do with you] aren't huge.
don't get me wrong, if, especially for maybe younger people who often dine in big groups, often with people they barely know, a vegetarian, teetotal, dieter, or whatever, should in no way be expected to subsidise other people's heavier consumption, no way, over their lifetimes this could quite easily add up to thousands of pounds' worth of pointless, undeserved, gifting. but in the circumstances you've described, yeah, best just to suck it up.