Hi there,
There are a number of causes of sudden death in sheep, and it can be so frustrating to see one you've been nurturing just give up.
The change in shape you describe could well be normal for getting close to lambing, or may have been stretching and tearing of abdominal muscles, but unusual if only her second lambing and carrying twins shouldn't be too much of a stretch.
The clear fluid from her nose/mouth could be suggestive of Jaagsiekte (sheep driving sickness or ovine pulmonary adenocarcinoma), which is a tumour of the lungs, and they can seem absolutely fine until they drop dead. To see if this is likely, pick up her back legs, it's called the wheelbarrow test. If copious fluid pours out, that is likely what it is. If the farmer sold them to you as healthy, but knows he has Jaagsiekte in the flock, that might be a bit naughty, but he may not know himself, and they do look absolutely fine until about to die.
If you are able, it might be worth getting the vet to do a quick on farm post mortem, as they'd be able to give you a rough idea of whether it is something like Jaagsiekte, or a pneumonia, or her abdominal muscles tearing etc. and whether it is likely something that could spread to the other ewe.
As regards her feeling full of fluid/air when you picked her up, the bacteria in the rumen that digest sheep's grass etc for them keep going when the sheep is dead, but the gut obviously doesn't churn the same, so they can build up an awful lot of gas in the stomachs after death, and that is likely what you felt.
So sorry for your loss, but hopefully the other one should be fine.
Suzanne