OP, I am glad you are receiving much-needed support from this thread. You sound like a wonderful new mama!
One of the hardest things for me - and for you, I suspect, from your post - is *having* to work when there is nothing I would rather do than be at home with my kids. For me it's not about work saving my sanity - I find it incredibly stressful to juggle home and a career - it's about work bringing in a much-needed financial contribution. We simply cannot afford to live on DH's salary alone (and believe me, we live a very modest lifestyle). There are no shortage of posts and threads (on this board, and many others), that suggest if you just planned better, if you would just re-use your tea-bag and make your beans from scratch, you could afford to stay home. Those are really hard conversations to hear, because they trigger my defenses and make me self-flagellate, thinking there must be something wrong with our family since WE couldn't make it happen.
We also have a very similar situation to yours - our DD is with one or both of us 4.5 days per week, and 2.5 days per week she is with our nanny. We are really proud of the fact that despite both of us working, our kiddos have never needed outside care more than 2 1/2 - 3 days per week. But still I feel the guilt. Tonight I have an unavoidable meeting with my board (I run a tiny non profit) that will get me home after 9 PM. (My older dd is already moaning and groaning about how I am "never home" and I know my younger DD, who is in a serious stage of mommy fixation, is going to be hell on wheels for my DH to put to bed in my absense.)
I work my behind off to be with my kiddos as much as I can, even if this means flexing my schedule so I'm writing grants at midnight from my home computer. It's freaking hard. I'm completely envious of the threads I see where SAHMs talk about never wanting or needing to go back to work, where SAHMS with school-aged kids have THIRTY plus hours of time ALONE per week, and then I'm on my grind of trying to make ends meet, burning the candle at both ends, never getting to relax, and trying to be the best mom I can.
When I am feeling gentle with myself, however, I think what you, and I, and all the parents who would LOVE to be home but who cannot afford to, are doing, is nothing short of heroic.
We love our families desperately and are doing the best job we can to support them, by bringing in much-needed income, all the while doing a mind-boggling juggling act. Hooray for us! Hooray for you!