"Anyhoo, I couldn't wrap my head around DH not wanting to stay home because, frankly, he financial contribution seemed paltry."
I was pretty stressed out about ever being the sole breadwinner. We purchased our house, a minivan (extremely helpful with the babies) and had the girls in the depths of the recession. Both the house and the van were purchased solely with what the banks were willing to give us based on my husband's salary alone and our cash downpayments (bit of a point of debate to finance any portion of the van at all -- as I like to keep larger cash reserves than my husband does).
Could we have the lifestyle we consider desirable if I were to lose my job? No. Could we keep the house, feed ourselves and cover the basic utilities? Yes. And that makes my life a lot less stressful.
I think alot of people don't realize that until they're in that position.
Op, I hope you and the nanny can work something out to make you both happy. In my opinion, your requests don't seem out of line.