Yes, sounds like a day at our house! I often wish I could take the batteries out!! And add a baby dd who is chasing me with books to read her and pointing at stuff she wants too, it gets real tiresome...fast!!
I do agree with the quiet time. I started quiet time when dd stopped napping at about 27 months. She goes in her room with books, some toys, animals, etc. I also worked it so the baby will go down for a nap at the same time. Introduce it slowly as ColinsMum said and keep it at the same time each day. And stick with it if she resists!! Tell her that you guys are going to try something new and that she's going into her room with her books, toys, etc. for some "xxx time" - call it what you want. Get her all comfy in her bed or where ever. Then you can say what you want - "Mama's going to rest." or "I'll check on you in a little bit." or "Ok, you are a big girl here!!"
Anything to make it sound like something "fun" that she will want to do daily.
Good luck!!