Try showering at night, when DH is home and toddler is sleeping?

I remember when Marieke was born, we had a few rough days. Fatigue, hormones, etc all come into play. Be prepared for that! No amount of organization and preparedness is going to stop you from having some days that are tearful. But you will be OK. I think most mums find that the first six weeks are the worst, and then you gradually establish a new routine, and life moves on so that you can hardly remember what it was like before.
Your toddler is probably going to be somewhat jealous of having to share her mummy too, and it is a hard adjustment for them. But personally, I think it is good for them to learn that the world does not revolve around their wants.
Maybe look into getting a baby carrier, like a hug a bub or ergo, or something. (I have a Moby for this new bub, which I am eager to try.) That way you can hold and comfort your newborn (even nurse them, sometimes!) with your hands free to do a little tidying, or sit with your toddler, or go for a walk, or whatever.
All the best!