What do you mean that the initial prior is "entirely wrong"? The prior is supposed to encode whatever information you have prior to seeing the data. It's only "wrong" if it fails to do that. A common way in which that can happen is overconfidence -- creating a prior that is unjustifiably narrow given the information you have.
Another common cause of unreasonable priors is because you lack an intuitive handle on what your model parameters mean. A strategy for dealing with that is to reparameterize in term of quantities that are more meaningful to your intuition. For example, a beta distribution is usually parameterized in terms of parameters $\alpha$ and $\beta$ that have no clear intuitive interpretation; reparameterizing in terms of the mean and standard deviation of the distribution makes it much easier to specify a reasonable prior.
If you still find a large mismatch between prior and likelihood, consider this a sign that something you thought was true isn't. Maybe there's a problem with your data collection. Maybe the process generating the data is different from what you thought, and you need to revise your model (not just revise parameter estimates). Or maybe your prior information was faulty, in which case Bayes' Rule creates a posterior distribution that reflects the appropriate compromise between your prior information and the new data.