welcome to the forum,
you might want to start looking at the unlock hub page on disclosure of police information on enhanced DBShttps://hub.unlock.org.uk/knowledgebase/local-police-information-2/
Speaking from experience you might find that you are going to need to seek legal representation from a solicitor in this matter, especially if your partner is still living at the same address as your self and your children.
As a person with a conviction for a sex offence involving images, when I was convicted in 2007, my offences where then placed on the enhanced DBS of my mother, father, brother and sister.
My parents and sister where involved in running guide and scout groups and my brother was an accredited FA referee with youth football.
The only way that they could get my convictions removed from there DBS was to make representations using a solicitor to the Met police and the independent monitor.
it was not a simple process and did take time, but with persistence the Met police decided that the information of my offences should not be disclosed on my family’s enhanced DBS checks.
there is nothing stopping you from being a teacher, the offence is not yours and you are not barred from teaching or on any bared lists, proving discrimination would be hard.
you might also want to make a subject access request to your local police force, and if the area your partners crimes were committed in is different to that police force as well, asking for all information they hold on you.
i hope that this give you some help,
you might also want to give the unlock helpline a call 01634 247350, or what’s app them 07824 113848 for further information, they are very good, they will treat your enquiry with the strictest of confidence and will not judge they are there to help.
Hope this gives you some areas to start looking