Hi OP.
I was the child in a relationship which was not as bad as yours with DH. My dad was what people today would call 'emotionally and verbally abusive'. He did the silent treatment, raging at inanimate objects, grim atmosphere, sudden explosions, insane rages.
My mum stayed with him till my youngest sister was 16 and I was in my mid-20s. From the earliest time I can remember, I didn't know why she was with him. Today, I can see that me and all my siblings are affected by the way we grew up. We are all damaged in some way.
My mum was in a similar situation to you - 4 DC, financially dependent up on v high-earning dad. She also did not want to sacrifice our lifestyles and the opportunities we had.
None of this is cut and dried. People who haven't lived in these situations will often act like it is. On the one hand, I did have a very privileged upbringing and that has helped me get where I am today. On the other, it has definitely damaged me and my siblings, probably forever.
I am not angry with my mum for not leaving. She was acting in her children's best interests. I am not angry with my dad for his behaviour (mostly). I now realise he is the product of a pretty horrific childhood himself. We actually have a very cordial relationship now.
However, having a baby myself now, NO WAY would I let her stay in any environment with such anger and tension. Today, my mum is often surprised by things I remember from my childhood. Those things will stay with your DC as much as the good material things your DH salary can provide.
I won't blame you whatever you decide to do. But I think personally you should consider the negative impact on your DC of staying where you are.
Why are you so anxious with the GP? Is it because you don't know how to approach your situation, or do you not want to talk about it with him? It's okay not to want to confide in him, even if he is a nice guy. If you want to seek help but not with him, you can brush him off and get it elsewhere - he doesn't 'own' your problems just because he is concerned.