Ruby- your daughter sounds like my son. He's 2.5 as well, and he cries - it feels like- every 5 minutes. Sometimes about really old things- like 4 days ago he fell and scratched his knee. It's barely visible, and I KNOW it doesn't hurt but today he collapsed on the floor wailing because he got a scratch on his knee. I also have no sympathy, and when he's wailing about something pointless and the baby is crying I always end up snapping at him. Unfortunately, whenever i snap, I say "I DON'T CARE!" Which my three year old is now mimicing whenever I try to get her to do anything. Yikes.
Sandy- we've been in this "no, mommy!" phase with both kids forever, I think. My DD has always been very mommy-attached, and my son just picked it up fairly recently. Recently it's- no, daddy will do it or YOU WON'T GET IT. Except I only say it that way when I'm about ready to scream. I try tor reason with them, or present it as an option- saying things like, "oh, you want juice? Well, you can wait until I put baby Everett in his bed or Daddy can help you get it now." Or I just delay and delay until my husband does it and the kids are thrilled because SOMEONE is finally listening to them.
For house stuff, I'm telling both kids "you need to play for a little while, I just need to wash these dishes and sweep and then I can do x,y,z with you. Okay? When I'm all done these things, we'll play." Or even more wind up- "we're going to eat breakfast, I'm going to clean and you can play or read books, and then we'll go to Grandma's house." They do the slump-shouldered "awww, okay" pouty thing, but they leave me alone for a little while anyway.
Things we're doing: new toys (dollar store, mostly). Sitting beside him while he plays with silly putty (note: don't EVER buy silly putty for a 2 year old. It's a terrible idea), new playdough, some stupid toy that will break in 5 minutes. I try to let him eat what he wants, within reason, to minimize fighting. Sitting on my lap whenever he can and making sure to add in lots of snuggles and time to be silly or get him laughing about something. We are definitely doing more TV then we did before unless there's another adult around to help out. Lots and lots of outside time.
Feliz- we are doing the same thing- we're trying to meet up with friends with kids as much as possible. Firstly because I need someone other than my husband to talk to, and secondly because when other kids are around the kiddos are much less "mommy, mommy, do this for me!" about everything every 5 minutes. Getting out makes a huge difference, and with more eyes to watch your exhausted brain can take a bit of a break and not worry about your kid wandering off.