An arm up the rectum will tell if there is a foal in there, especially since she is bagging up. Takes maybe 10 minutes from putting on the glove, lubricating it, inserting arm, removing poop and reinserting arm again and practically bopping baby on the head.
A blood test will involve getting the blood, taking the blood back to the clinic, either sending blood off or running test and then reading test and calling you. Hours at best, days at worst.
Get a new vet, have the horse palpated and then you will know. Or wait till Monday with the first vet who sounds like he/she doesn't want to deal with it and hopes the mare will have the baby by then.