I am a barrister and not a solicitor, so my experience is with pupillage recruitment and not training contracts, which is a caveat from the outset. But there are relatively few solicitors giving advice on here at the moment, so I thought I'd weigh in. Generally speaking, the advice would be not to retake A-Levels but to look forwards and concentrate on getting better results from this point on. However, there are two aspects here that make me think you're an exception to that general advice. The first is that you have mitigating circumstances. That's an automatic pass in situations like this. The circumstances have to be genuinely mitigating, and you also need to be able to demonstrate a higher level than the results you've obtained to this point. You seem confident that you can demonstrate a significantly higher level, which makes me think both that your circumstances are genuinely mitigating, and that absent those circumstances you could achieve excellent A-Level results, and probably an excellent academic standard generally going forwards.
For those two reasons I think it probably is a good use of your time here to take the year out to resit your A-Levels, assuming you are confident you can achieve AAA. Any experience you can gain in that time is a bonus, but one year is not very long in the context of your academic career, and indeed your career more generally. Taking that year to bump your A-Levels up to AAA is something that I think is worth it. Yes, you may well still fall foul of those recruitment processes that take your original grades, or which are automated and may not be able to appreciate mitigating circumstances, but that's something you'll always have to contend with. In the round, I think it will be beneficial to go into your degree with AAA at A-Level. It will leave whoever reads your application in no doubt at all both that your circumstances are mitigating and that your true level is much higher, and indeed one assumes that you will then be able to maintain that standard through your degree with a high 2:1 or First.
So yes, in the round I think in your case this is worth it. However, if any solicitors with experience of training contract recruitment do see this thread and don't agree with me, it is most certainly worth listening to them.