Lawyer up and sue. I'm assuming you're American because you referenced Experian. FCRA gives you two years.
Equal chances of success as suing them but considerably less expensive.
Also considerably more likely to get you arrested, possibly with overwhelming force.
Which could possibly cause media attention and Internet outrage, so it still feels like a better option than suing.
It took months to fix the address thing and still ten years later I cannot get them to competently resolve the "being financially linked" data error. Sure this was a data provider that caused the problem and they should be responsible for fixing it. But in the end it became impossible to fix because there is no single department in the bank through which the credit record data is passed.
Trying to work with the credit scoring agencies was futile because they just bounce you back to the data provider telling you to tell them to fix their data.
It's like living the the world of Terry Gilliam's Brazil.
(this should be obvious, but just to be sure: IANAL)
Send them a letter where you give them 1 month to resolve the problem, providing full documentation that you are divorced and point that as such the information is incorrect, and that under the Data Protection Act they are legally obliged to ensure incorrect personal information about you is amended or deleted. If you have past correspondence with them where they acknowledge the information is incorrect, then provide copies.
Inform them that if the matter is not resolved, or they have contacted you to agree on how to resolve it, within 30 days, you will file a formal complaint with the Information Commissioner (ico.org.uk).
Provide the same notification to the bank (ensure it is addressed to the legal department).
The credit scoring agencies has a legal obligation under the Data Protection Act to ensure personal information is correct. This applies to all organizations subject to EU data protection rules (which is pretty much everyone with very limited exceptions). That the data comes from a third party is not an excuse if you have provided documentation that the information is wrong. (it may be reasonable that they refer you there first, but if you have tried to get the bank to fix it, and they've not, then it is not reasonable for them to continue to insist).
Ultimately, if even the ICO can not get them to budge, go to a lawyer. Failure to rectify this information is blatant violation of the principles of the Data Protection Act, and you can get a court order to have the information corrected, and in some cases even require that they contact every recipient of the flawed information.
In your case this is important. If either one of you goes bankrupt e.g. you risk the other ones credit score being ruined for about a decade. But frankly, in most cases a threat about a complaint to the ICO ought to be enough. If you've written a letter and complained to ICO, and they fail to correct the information, then a court case will be a walk in the park.
Also note that in certain circumstances you may be due damages incurred as a result of the incorrect information.
See: http://ico.org.uk/for_organisations/data_protection/the_guid...
A last consideration: The Data Protection Act also provides you with some means of insisting that certain types of decisions are not taken automatically, or to have automated decisions reconsidered. This provides you a fallback if e.g. you are often refused credit based on automated scoring based on the flawed data. You can notify the bank in advance in writing that you do not consent to automated decision making, and providing documentation of the divorce, or you can demand a manual reconsideration afterwards (and provide the same documentation).
Under EU data protection laws, in most cases failure to provide you a way to delete or amend incorrect personal information held about you is a clear violation of the law. As is failure to grant you access to information about whom they have passed personal information about you on to.
That doesn't mean they won't try to act like asses sometimes, but bringing up the Data Protection Act and mention a complaint to the Information Commissioner can and does make a difference.