Aww OP I am so sorry to hear you are under so much stress and this hasn't helped.
It is really easily done when you send a lot of emails every day. Usually what happens is someone starts typing a name eg "Julia" for "Julia Morris" and then hits enter to autocomplete the rest, not realising the top name on the list is actually "Julia Metcalfe" or because that's the most recent contact. When that happens, yes they will know who that recipient is and you can ask. They can't tell you who exactly but may be able to tell you whether it's a staff member, client, professional colleague, Land Registry clerk- whatever. The chances are high that it was sent to another professional contact either in the office or externally (who has to deal with GDPR in their own right) who will have glanced at it, realised it's not for them and deleted it either before making the sender aware, or after the sender realised their mistake and notified the recipient.
The other alternative (less likely) is that the sender was typing out an email address and mistyped eg Anne.Thompson for Anne.Thomson. In this case, they'd be highly unlikely to have any idea who or where this person might be.
In both cases they will have written to the recipient as soon as the error was realised and asked them to delete the email without reading it. As it's an unconnected party, albeit for very sensitive information, and presumably nothing that could be used against you, it will be a lower risk than if it was sent to someone involved in the case.
Compensation for this is likely to be in the hundreds, not thousands, as it's been very distressing but has not resulted in financial loss or injury to you. If it did not involve a sensitive situation it might be worth £50 or 100 - as you say "a couple of hours" I'm guessing it's closer to 300-500, which is an indication that they consider it sufficiently serious.
You can complain to the ICO about the breach if you like - you are perfectly within your rights to do so. However unless the breach was malicious or part of a pattern of negligence or poor data protection practices, the ICO is not likely to take any action as the firm has taken steps to inform you and to remedy the breach, and the ICO cannot award compensation. It may impose fines, but, because it's a fact of life that accidents happen, this is also unlikely unless the breach was part of a pattern of negligence or malicious behaviour.
I know this has been very upsetting for you. And I hope it doesn't continue to distress you once you've had a chance to absorb it. I would suggest you accept the cash and keep it to treat yourself to something when this is all over. It sounds like you're going through a really tough time. X