Leaving the issue of a third child aside... I was in your shoes 9 months ago, I have 2 toddlers and we both worked full time. I was the only parent who could get slightly flexible hours so I shouldered all pick ups, sick days etc. not only did my boss (actually both our boss) hate me for it, we knew that if DH did any of it he would get tarred too. It was making me very ill, trying to juggle work and being there for the kids. Work were pushing me out the door and I left to become a sahm.
Anyway I had the same fears of going mad at home, and yes I would go mad at home on my own with 2 toddlers asking 'why?' And 'MUMMY!!!' Every 5 minutes, so I made a very special effort to get out every day, meet people (not just mums) and become part of the community.
I know any job I have in the future will probably never pay the same, but I don't care anymore.
We have got insurance for ill health and death for both of us, and DH has income protection insurance. These things help cover the worst situations. We have made a concerted effort to pay of all our debts apart from mortgage and we have a monthly budget which gives enough slack to cover things like a new tyres etc. we also have a savings cushion for big emergencies. DH also has a good enough pension scheme to cover both of us when he retires.
I would not recommend quitting or expanding your family without sound financial planning, especially in light of the budget. Think about the worst scenarios and what you would do.