The first three months with a newborn can be hell, no matter how ideal the situation is. Its overwhelming!!!!! However, THAT does go away as they age! :)
Get your nap. Bring 8 year old inside and have her do something quiet for at least 30 minuets (set a timer) so you can lay down, even if you don't sleep you will rest. An 8 year old does not have the right to play all day long! They need to be your little helper, and an 8 year old can do a TON of stuff! Teach her how to pick up the messes in the house, even to use a vacuum (my 3.5 year old is learning this now, its just a bit heavy), or dusting. Washing dishes (again my 3.5 year old LOVES to do this, and she's kinda good at it, but I'm sure will be independent at it when she's 8). You are not a mean mommy to require your daughter to help you around the house. She's not a princess and you the maid! Everyone in the household needs to work to keep it clean and functional. You are giving her a GIFT, a good work ethic, that will benefit her the REST OF HER LIFE. Just because you didn't know better when she was younger does not mean you can bring things into line now.
The sibling rivalry is very common (I don't like to use the word normal because it has the connotation that you don't need to address it and it will go away on its own - not true!). My 2.5 year old did many of the same things when the baby came home. She was not as expressive, but acted out a lot! Very destructive, regressed on potty training, mean to baby... I made the mistake of not dealing with a lot of the issues and now a year later my 3.5 year old is a HAND FULL! We've made a lot of progress with a zero tolerance on being rebellious. This includes saying no, ignoring me, doing something similar to what I asked - but not quite what I asked, hitting/kicking/pinching, screeching, talking back, being negative, etc... It took about 6 weeks to get things under control again (meaning not spending ALL DAY) doing it. My biggest advise would be, don't let her get away with stuff while you're nursing! Better to put down a screaming baby and deal with rebellion immediately, then to wait 30 min for baby to eat and fall asleep before dealing with it.
Anyway, I know that this sounds exhausting and you're already exhausted, but investing some training in the big sister will pay off!
Best wishes!