That's a shame when they fall out, it could be that Bigwig could still be very wary as he's been manhandled over the last few days and is still a bit frightened so is taking it out on Coco. He could still be in pain, I take it you were sent home with pain relief to give him?
If possible, as tonibun suggested, putting them in a new, neutral space may help, as it will be new territory for both of them so they can explore it together and hopefully that will repair the bond.
In future though, may I suggest that if one of your bunnies has to be hospitalised, you take both. Most, if not all, vets will accept a bonded pair to look after, even if it only the one which needs treatment, as they know how delicate the bond can be. I always take both of mine to the vet, even if it's just for a check-up, and if one is ill and has to stay overnight, then they both stay together.
I hope that Coco and Bigwig rebuild their bond soon for you.