I'm former SLT of a large school, pastoral including staff pastoral and union rep.
I'm afraid to tell you that your solicitor is incorrect and I suggest that you find another one.
A driving ban will show up on your DBS.
Please see here under the heading More Serious Offences.
I have seen many things show up on a DBS.
@Hammondhugh SLT are human, not Gods and not untouchable, they have their own lived experiences, they have families.
Inform the Head asap, it is better that you tell them than they find out during a routine DBS check.
Write down what you will say, if you can provide evidence of the relative's hospital stay and any other relevant evidence, do.
Be clear.
Be contrite.
They will understand, it does happen with reasonable frequency.
If you are banned for the maximum number of days and getting to work will be difficult find an Airbnb or, if you know someone, ask a local colleague if you can stay in return for a small payment.
This is written assuming that this is your first offence?
Please don't do it again.