After thinking longer about this. I wonder if maybe you should corral the two together but with a fence between them for a time. This would give the mule a chance to get used to it and realize it's not a predator.
We did this when introducing our newest cat "Stewie" to the very appropriately named "Gimli" (kind of crusty in a friendly way and afraid of nothing.) We knew Gimli wouldn't take kindly to a new kitten at first so we kept Stewie in another room for a while where he eagerly presented his paws to Gimli under the door to play but Gimli just sat there and growled and hissed for a few days. Eventually, he got used to the scent and the idea of a new animal in the house and we slowly put them together. Now they are the best of friends.
If the mule can't be spared from coyote duty, then perhaps just fence off the calf somewhere still accessible. I know it's not "open range" for him at that point but it beats getting bitten in the ass by an ass.
