The very fact that the OP is frightened of him finding out makes me believe that there is financial abuse going on, tbh. There's
Having only £600 a month to pay for all the food, toiletries, cleaning stuff, some of the outgoings and most of the clothes for a family of 4 (two of whom are teens, who eat huge amounts and grow out of their clothes), and pay some of the bills is outrageous when her partner is bringing home somewhere around £3.5-4k a month is abusive too, imo.
I think you need to be very frank with him, OP, and explain that the money you get from him isn't enough to pay for all the things you have to pay for. Make a list of everything you pay for and how much, including irregular spending like clothes and total it up, so he can see that isn't enough. Don't forget to include things like school uniform, dinners and trips. Remind him that you can't get a job because the only work you could do would involve working weekends, and he doesn't want you to do that.
Do you think he spends much on himself or his car?
Don't fret about the DEA unless he asks you directly if you know what it might be for. If he does, only you can judge whether or not it would be best to own up that this could be a TC overpayment from years ago. If you do, and he frightens you, just leave, go to a friend's or family member.
Also speak to Women's Aid and see what they say.
If you did leave, you'd be entitled to Universal Credit and some maintenance from him. And the maintenance wouldn't come into the UC calculation, so you'd still get full UC until you manage to finds a job.
My ExH was financially (and emotionally) abusive and I know how fearful it makes you feel. And how liberating it is to get out of that relationship.
Good luck.