A hearse was a farm tool before it was a funeral car.
Etymonline dates the English word to around 1300, when it meant a flat framework for candles hung over a coffin. It comes from Old French herse, which meant a harrow, a portcullis, or a large church chandelier. The Old French goes back through Medieval Latin to Latin hirpex, a rustic word for a harrow, the spiked frame dragged over a field to break up soil.
The funeral frame was named for its resemblance to a harrow. Merriam-Webster describes the medieval French candle frame as triangular, like the farm tool. Etymonline notes that the earliest use is in late 13th century Anglo-Latin, and Merriam-Webster dates the English word to the 14th century, so the date depends on the source.
The wolf comes in at the very back of the story. Etymonline says hirpex may come from Oscan hirpus, "wolf," perhaps because the harrow's teeth resemble a wolf's. It adds that the Oscan word may instead be related to Latin hirsutus, "shaggy, bristly." So the wolf is a guess, not a settled fact.
The meaning then moved outward. Etymonline says the word broadened to other temporary structures built over the dead. Merriam-Webster says the sense shifted to a platform for a coffin and then to a vehicle. By the 1640s, per Etymonline, it meant a vehicle carrying a body to the grave.
The same root gave English a very different word. Etymonline says rehearse comes from Old French rehercier, "to go over again," literally to rake or harrow again. Grammarphobia agrees that it shares the Old French source herce with hearse. It came to mean repeating or retelling something, and from the 1570s practicing a performance. Every actor who rehearses is, in the oldest sense, harrowing a field again.
Hearse and rehearse therefore share a farm tool. One went to the funeral and the other went to the theater.