To do the job properly, I would think you'd need a specialist, and I suspect the resultant bill would not be small - a lot of the tub would have to come apart to get to it.
If it were me and I found myself at a pecuniary disadvantage, I'd probably use liquid epoxy wood repair to stabilise and harden the existing wood, drill and inject a few boron rods to kill off any rot and prevent any new occurrence, screw a strengthening piece below or behind it to restore the strength, and re-form the profile with epoxy to make it look neat again.
If they can use epoxy injection and boron rods to fix roof timbers in houses, it should be ok for a non-critical body frame component, I would have thought.
