Our kids are 17 months apart. Our son is 3.5 years (4 in January) and our daughter is 2 years (2.5 in January.)
It is nothing but pure chaos. Our son started part time pre-school last week, so I finally have quality time with our daughter for 3 hours in the morning. Honestly, I can't take them to the grocery or park by myself. You shouldn't feel bad, I think it is just the age of the kids right now. As our son gets closer to being 4 he is starting to tantrum less and listen and help more. They have both always stayed home with me, and sending our son to pre-school was the best thing for him. He needed his "alone" time.
Things are different in our house since he went to pre-school last week. We are still trying to find a schedule. But right now it is something like this. He wakes up at 7, there is no tv or playing in the mornings because we have to be out the door by 8. I clean house when L. sister and I get back home or do errands. I pick him up at 11:30, he and his sister watch tv while I cook lunch, then it is right off to naps for both of them. One always wakes up before the other, on any given day it is a toss up of who it will be. So which ever one wakes up, we get some quality play time in before the other gets up. If our son wakes up, he can do fun things that he can't do when L. sister is around like painting, play-doh, crafts, or we will work on his writing and spelling in his work books. When the other one wakes up I usually let them sit on the couch and watch some tv while they wake up and I pick up toys or do dishes or something. We haven't been able to go outside due to the Missouri heat, but that will be changing soon. In the summer we would go swimming after naps, either in the back yard or the public pool, soon we will be playing in the back yard after naps but it probably won't be every day because I am 7 months pregnant and can't chase them easily or carry them anymore. Dad works nights, and is usually awake around dinner time, so he is usually the one to cook dinner (I am so lucky my husband loves to cook.) He will play with the kids, or give them baths while I clean up the kitchen. After baths they usually destroy the living room by getting all of their toys out, I clean it up when they are both in bed.
The kids do fight, I understand what you mean when you say you can't do it anymore. I was to that point and then pre-school started. It gave me the break I needed to be the Mom I knew I could be and used to be. Have you thought about putting your daughter into pre-school?