Sheis it depends on your contract. At a lot of larger employers (especially in the City) the first few weeks at least would be on full pay.
You would need to ask the Nanny to take the DC out of the house for a large part of every day to give you a break (I agree about not knocking about together as that would be only stressful). Is that feasible?
Or you would need to go away. Sigh, I am sure that would be tricky if your DH couldn't be back in time each night - working mums don't get a break, do they, but then he would HAVE to cope if you were not around and would HAVE to figure it out so all things are possible.
I am glad you have spoken to a mentor. I hope he/she is equipped to give you good advice.
Lastly, I really don't think an employer would ever sack you for being off work for a few months for stress - they are more likely to be worried about you suing them for being the partial cause - but, even if they did (they won't) in the round, ANYTHING will be better than you continuing to feel this low.
I also remember being worried about money if I gave up work, but somehow things worked out. If you are employing a Nanny then I am guessing that both you and your DH earn reasonably and that you don't have massive debts (sorry, big assumptions) and somehow you would get by if you need to. This might just be a time that you use up some of your savings and can rebuild them in the future.
Take care. I am unusually out all day tomorrow so won't be posting for most of the day but will check on you tomorrow night at the latest.
Have a good evening. Cuddle those lovely children and go easy on yourself :-)