I'm a mother, diagnosed with schizoaffective disorder, and nobody has accused me of being a bad parent, or informed social services of my condition at all. So in that regard I think you're okay. I'm also not allowed to drive, but that's not something that bothers me, since unlike you I'm a terribly unsafe driver... I see things on the road that aren't there, which makes for an interesting experience.

You can explain to a pdoc why you need to drive... I don't think the DVLA will find out if your doctor has said he'll not tell them. But look into it.