It depends what DBS you are getting - because it’s with kids it will be enhanced and possibly with barred list. It’s not really so much about whether or not you are teaching but whether or not you will be unsupervised with them, how long for, and especially doing personal care. I have to order DBS checks as part of my job and have had one myself working w vulnerable kids so I know a bit about this but not loads.
The only time it’s illegal to employ you is if you have done something which would put you on the barred list which you haven’t (to simplify it, those offences entail violent or predatory behaviour, esp towards kids). It’s up to the employer’s discretion beyond that. The Mind website says that a theft will always show up, and an enhanced dbs can pull up an arrest even without caution - the police may or may not put it on there if they think it is pertinent. I would expect it to be on there tbh, but I don’t think it would be normal for this to cost you the job.
If they give you an offer pending the DBS, I would ask to speak to the employer at XYZ time (ie make time to discuss it) and just lay it on the table. Better to get it off your chest and in a composed, reflective way than be caught off guard. They’ll appreciate that you are being straight with it I think, esp. if you emphasise it’s been years since and you have had no trouble aside from that - and if you say you’d understand if this would stop them from hiring you, Realistically SLT now have to have a strong understanding of social work principles so they will probably be sympathetic. When I worked at a school a couple people working as TAs had much more recent convictions for weed possession which showed up on the DBS and it was fine following a considered conversation with SLT.
TL;DR: chances are it will come up, but it’s not illegal to employ you - best to preempt it and raise it with them in a considered way, and it will probably be OK.